96f0f4fe0959213c30e402766239e137 joudifequ_a2025m1v416Part2p1071-1098.pdf 4959b7c2457783c4a168bcbb0f6e485dc6960e74 joudifequ_a2025m1v416Part2p1071-1098.pdf a6e61592edd6b97f3c4c0f328e78582b6a82b75bc89151a937e0efeff8761d35 joudifequ_a2025m1v416Part2p1071-1098.pdf Title: More limit cycles for complex differential equations with three monomials Subject: Journal of Differential Equations, 416 (2025) 1071–1098. 10.1016/j.jde.2024.10.013 Author: M.J. Álvarez Creator: Elsevier Producer: Acrobat Distiller 24.0 (Windows) CreationDate: Wed Nov 27 09:08:43 2024 CET ModDate: Wed Nov 27 09:08:43 2024 CET Custom Metadata: yes Metadata Stream: yes Tagged: yes UserProperties: no Suspects: no Form: none JavaScript: no Pages: 28 Encrypted: no Page size: 467.717 x 680.315 pts Page rot: 0 File size: 419372 bytes Optimized: yes PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- OGCFPH+Helvetica Type 1C WinAnsi yes yes no 921 0 OGCFPI+VAGRoundedStd-Bold Type 1C Custom yes yes yes 922 0 OGCFPJ+Times-Roman Type 1C Custom yes yes no 923 0 OGCGAK+MTMI Type 1C Custom yes yes yes 924 0 OGCGAL+MTSYN Type 1C Custom yes yes yes 925 0 OGCGAM+Times-Italic Type 1C Custom yes yes no 926 0 OGCGBM+Times-Bold Type 1C MacRoman yes yes no 927 0 OGCGBN+MT2HRBT Type 1C WinAnsi yes yes no 928 0 OGCGBO+Symbol Type 1C Custom yes yes yes 929 0 OGCGEO+MTEX Type 1C Custom yes yes yes 295 0 OGCGHO+wasy10 Type 1C Custom yes yes no 301 0 OGCGNN+CMSY10 Type 1C Custom yes yes yes 305 0 OGCKJH+MSAM10 Type 1C Custom yes yes no 309 0 OGCKNG+MTMIB Type 1C Custom yes yes yes 310 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-02-14 02:53:44 CET RepresentationInformation: joudifequ_a2025m1v416Part2p1071-1098.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-02-13 20:37:06 CET Size: 419372 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf Profile: Linearized PDF PDFMetadata: Objects: 985 FreeObjects: 385 IncrementalUpdates: 1 DocumentCatalog: PageLayout: SinglePage PageMode: UseOutlines Language: en Outlines: Item: Title: More limit cycles for complex differential equations with three monomials Destination: yjdeq12894.title.0:1 Children: Item: Title: 1 Introduction and main results Destination: yjdeq12894.section.1:2 Item: Title: 2 Proof of Theorems A and B Destination: yjdeq12894.section.2:11 Item: Title: 3 Proof of Theorem C Destination: yjdeq12894.section.3:12 Children: Item: Title: 3.1 Lower bounds for the number of limit cycles Destination: yjdeq12894.subsection.1:13 Item: Title: 3.2 Upper bounds for the number of limit cycles Destination: yjdeq12894.subsection.2:17 Item: Title: 3.3 Proof of Theorem C Destination: yjdeq12894.subsection.3:22 Item: Title: 3.4 On the open cases in Table 1 Destination: yjdeq12894.subsection.4:23 Item: Title: 3.5 Other approaches to generate limit cycles for QS Destination: yjdeq12894.subsection.5:28 Children: Item: Title: 3.5.1 Higher order Melnikov functions Destination: yjdeq12894.subsubsection.1:29 Item: Title: 3.5.2 Perturbation of non-linear centers Destination: yjdeq12894.subsubsection.2:31 Item: Title: Acknowledgments Destination: yjdeq12894.section.3:32 Item: Title: Appendix A General expression of the first Lyapunov quantity L1 and Andronov--Hopf type bifurcations Destination: yjdeq12894.appendix.1:33 Item: Title: Data availability Destination: yjdeq12894.section.3:39 Item: Title: References Destination: yjdeq12894.section.3:40 Info: Title: More limit cycles for complex differential equations with three monomials Author: M.J. Álvarez Subject: Journal of Differential Equations, 416 (2025) 1071 1098. 10.1016/j.jde.2024.10.013 Creator: Elsevier Producer: Acrobat Distiller 24.0 (Windows) CreationDate: Wed Nov 27 09:08:43 CET 2024 ModDate: Wed Nov 27 09:08:43 CET 2024 ID: 0xad9205ec76c824df9b7670f335166a1a, 0x00334fa62076794a9d423c42f5d761e5 Filters: FilterPipeline: FlateDecode FilterPipeline: CCITTFaxDecode Images: Image: NisoImageMetadata: FormatName: image/tiff CompressionScheme: CCITT Group 4 ImageWidth: 786 ImageHeight: 563 BitsPerSample: 1 BitsPerSampleUnit: integer ImageMask: true Fonts: Type1: Font: BaseFont: OGCGBN+MT2HRBT FontSubset: true FirstChar: 67 LastChar: 82 FontDescriptor: FontName: OGCGBN+MT2HRBT Flags: Serif, Nonsymbolic FontBBox: -75, -287, 1121, 777 FontFile3: true Encoding: WinAnsiEncoding Font: BaseFont: OGCGBO+Symbol FontSubset: true FirstChar: 2 LastChar: 2 FontDescriptor: FontName: OGCGBO+Symbol Flags: Symbolic FontBBox: -180, -293, 1090, 1010 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCGEO+MTEX FontSubset: true FirstChar: 2 LastChar: 14 FontDescriptor: FontName: OGCGEO+MTEX Flags: Symbolic FontBBox: 20, -2954, 1365, 46 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCGHO+wasy10 FontSubset: true FirstChar: 2 LastChar: 2 FontDescriptor: FontName: OGCGHO+wasy10 Flags: Symbolic FontBBox: -23, -1667, 1720, 752 FontFile3: true EncodingDictionary: Differences: true Font: BaseFont: OGCGNN+CMSY10 FontSubset: true FirstChar: 67 LastChar: 86 FontDescriptor: FontName: OGCGNN+CMSY10 Flags: Symbolic, Italic FontBBox: -29, -960, 1116, 775 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCKJH+MSAM10 FontSubset: true FirstChar: 2 LastChar: 2 FontDescriptor: FontName: OGCKJH+MSAM10 Flags: Symbolic FontBBox: 7, -463, 1331, 1003 FontFile3: true EncodingDictionary: Differences: true Font: BaseFont: OGCKNG+MTMIB FontSubset: true FirstChar: 76 LastChar: 76 FontDescriptor: FontName: OGCKNG+MTMIB Flags: Serif, Symbolic, Italic, ForceBold FontBBox: 0, -250, 994, 706 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCFPH+Helvetica FontSubset: true FirstChar: 32 LastChar: 119 FontDescriptor: FontName: OGCFPH+Helvetica Flags: Nonsymbolic FontBBox: -166, -225, 1000, 931 FontFile3: true Encoding: WinAnsiEncoding Font: BaseFont: OGCFPI+VAGRoundedStd-Bold FontSubset: true FirstChar: 68 LastChar: 116 FontDescriptor: FontName: OGCFPI+VAGRoundedStd-Bold Flags: Symbolic, ForceBold FontBBox: -151, -310, 1060, 939 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCFPJ+Times-Roman FontSubset: true FirstChar: 30 LastChar: 241 FontDescriptor: FontName: OGCFPJ+Times-Roman Flags: Serif, Nonsymbolic FontBBox: -168, -218, 1000, 898 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: OGCGAK+MTMI FontSubset: true FirstChar: 2 LastChar: 122 FontDescriptor: FontName: OGCGAK+MTMI Flags: Serif, Symbolic, Italic FontBBox: 0, -213, 987, 680 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCGAL+MTSYN FontSubset: true FirstChar: 2 LastChar: 177 FontDescriptor: FontName: OGCGAL+MTSYN Flags: Symbolic FontBBox: 0, -954, 1043, 900 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: OGCGAM+Times-Italic FontSubset: true FirstChar: 30 LastChar: 242 FontDescriptor: FontName: OGCGAM+Times-Italic Flags: Serif, Nonsymbolic, Italic FontBBox: -169, -217, 1010, 883 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: OGCGBM+Times-Bold FontSubset: true FirstChar: 40 LastChar: 222 FontDescriptor: FontName: OGCGBM+Times-Bold Flags: Serif, Nonsymbolic, ForceBold FontBBox: -168, -218, 1000, 935 FontFile3: true Encoding: MacRomanEncoding Pages: Page: Label: 1071 Annotations: Annotation: Subtype: Link Contents: URI link to http://crossmark.crossref.org/dialog/?doi=10.1016/j.jde.2024.10.013&domain=pdf Rect: 114, 613, 143, 622 Annotation: Subtype: Link Contents: URI link to http://www.sciencedirect.com Rect: 222, 636, 300, 644 Annotation: Subtype: Link Contents: URI link to https://doi.org/10.1016/j.jde.2024.10.013 Rect: 140, 590, 320, 598 Annotation: Subtype: Link Contents: URI link to http://www.elsevier.com/locate/jde Rect: 341, 579, 433, 587 Annotation: Subtype: Link Contents: Link to named destination addressa0.label Rect: 176, 476, 180, 488 Destination: 868 Annotation: Subtype: Link Contents: Link to named destination corthanks.label Rect: 182, 476, 187, 488 Destination: 868 Annotation: Subtype: Link Contents: Link to named destination addressa0.label Rect: 233, 476, 237, 488 Destination: 868 Annotation: Subtype: Link Contents: Link to named destination addressb0.label Rect: 295, 476, 300, 488 Destination: 868 Annotation: Subtype: Link Contents: Link to named destination addressc0.label Rect: 302, 476, 306, 488 Destination: 868 Annotation: Subtype: Link Contents: Link to named destination addressa0.label Rect: 371, 476, 376, 488 Destination: 868 Annotation: Subtype: Link Contents: URI link to http://creativecommons.org/licenses/by/4.0/ Rect: 53, 229, 210, 237 Annotation: Subtype: Link Contents: URI link to mailto:chus.alvarez@uib.es Rect: 122, 105, 187, 113 Annotation: Subtype: Link Contents: URI link to mailto:tomeu.coll@uib.cat Rect: 240, 105, 302, 113 Annotation: Subtype: Link Contents: URI link to mailto:armengol.gasull@uab.cat Rect: 336, 105, 417, 113 Annotation: Subtype: Link Contents: URI link to mailto:rafel.prohens@uib.cat Rect: 90, 95, 161, 103 Annotation: Subtype: Link Contents: URI link to https://doi.org/10.1016/j.jde.2024.10.013 Rect: 51, 76, 181, 84 Annotation: Subtype: Link Contents: URI link to http://creativecommons.org/licenses/by/4.0/ Rect: 53, 56, 193, 64 Page: Label: 1072 Sequence: 2 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.AGP Rect: 420, 489, 427, 497 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GLT Rect: 317, 477, 329, 485 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GZ Rect: 148, 453, 160, 461 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-lc-A.label Rect: 93, 416, 102, 425 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination thm-lc-B.label Rect: 123, 416, 130, 425 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination cite.GLT Rect: 344, 417, 356, 425 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.Andronov Rect: 340, 344, 347, 352 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-ap-D.label Rect: 107, 319, 115, 328 Destination: 218 Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 134, 319, 141, 328 Destination: 236 Page: Label: 1073 Sequence: 3 Annotations: Annotation: Subtype: Link Contents: Link to named destination eq_main.label Rect: 320, 488, 333, 497 Destination: 61 Annotation: Subtype: Link Contents: Link to named destination cite.Cop0 Rect: 207, 381, 214, 389 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.CW Rect: 118, 370, 125, 378 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.S Rect: 125, 370, 137, 378 Destination: 285 Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 269, 212, 275, 221 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination tb:2.label Rect: 295, 212, 301, 221 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination thm-lc-B.label Rect: 308, 117, 316, 126 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination thm-lc-C.label Rect: 334, 117, 342, 126 Destination: 13 Annotation: Subtype: Link Contents: Link to named destination le:equi.label Rect: 150, 69, 164, 78 Destination: 124 Page: Label: 1074 Sequence: 4 Annotations: Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 115, 373, 121, 382 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination cite.GLT Rect: 419, 350, 431, 358 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination pr:3.11.label Rect: 401, 337, 420, 346 Destination: 159 Annotation: Subtype: Link Contents: Link to named destination se:uni.label Rect: 82, 325, 95, 334 Destination: 124 Annotation: Subtype: Link Contents: Link to named destination se:new.label Rect: 192, 289, 205, 298 Destination: 186 Annotation: Subtype: Link Contents: Link to named destination pr:mel.label Rect: 142, 253, 160, 262 Destination: 196 Annotation: Subtype: Link Contents: Link to named destination se:falta.label Rect: 106, 217, 127, 226 Destination: 196 Annotation: Subtype: Link Contents: Link to named destination thm-lc-A.label Rect: 144, 193, 152, 202 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination thm-lc-B.label Rect: 172, 193, 180, 202 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination thm-lc-A.label Rect: 128, 169, 136, 178 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination ec-ej-n.label Rect: 211, 83, 225, 92 Destination: 25 Page: Label: 1075 Sequence: 5 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.GLT Rect: 160, 584, 172, 592 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 273, 467, 280, 476 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 164, 394, 171, 403 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination ec-ej-n.label Rect: 206, 322, 219, 331 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination coro.label Rect: 131, 310, 149, 319 Destination: 232 Annotation: Subtype: Link Contents: Link to named destination ec-ej-n.label Rect: 382, 286, 396, 295 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination ec-ej-n.label Rect: 407, 274, 420, 283 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination thm-lc-B.label Rect: 128, 214, 135, 223 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination cite.YuHanYuan Rect: 130, 130, 142, 138 Destination: 285 Page: Label: 1076 Sequence: 6 Annotations: Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 139, 607, 146, 616 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination coro.label Rect: 379, 583, 397, 592 Destination: 232 Annotation: Subtype: Link Contents: Link to named destination ec-ej-n.label Rect: 368, 475, 382, 484 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination prop-quad.label Rect: 294, 330, 308, 339 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination prop-quad.label Rect: 138, 281, 152, 290 Destination: 1 Annotation: Subtype: Link Contents: Link to named destination eq_main.label Rect: 268, 281, 282, 290 Destination: 61 Annotation: Subtype: Link Contents: Link to named destination QS-2cl.label Rect: 68, 269, 81, 278 Destination: 61 Page: Label: 1077 Sequence: 7 Annotations: Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 164, 559, 171, 568 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination eq_3.label Rect: 417, 334, 430, 343 Destination: 51 Annotation: Subtype: Link Contents: Link to named destination thm-lc-C.label Rect: 140, 250, 148, 259 Destination: 13 Page: Label: 1078 Sequence: 8 Annotations: Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 145, 547, 152, 556 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination cite.CGM Rect: 52, 289, 59, 297 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 173, 118, 180, 127 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination coro.label Rect: 239, 118, 257, 127 Destination: 232 Page: Label: 1079 Sequence: 9 Annotations: Annotation: Subtype: Link Contents: Link to named destination coro.label Rect: 221, 487, 240, 495 Destination: 232 Annotation: Subtype: Link Contents: Link to named destination coro.label Rect: 181, 392, 200, 401 Destination: 232 Annotation: Subtype: Link Contents: Link to named destination eq_main.label Rect: 144, 308, 157, 317 Destination: 61 Annotation: Subtype: Link Contents: Link to named destination QS-2cl.label Rect: 255, 308, 268, 317 Destination: 61 Annotation: Subtype: Link Contents: Link to named destination prop:1+1.label Rect: 269, 272, 283, 281 Destination: 67 Annotation: Subtype: Link Contents: Link to named destination thm-lc-C.label Rect: 261, 260, 269, 269 Destination: 13 Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 99, 236, 105, 245 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination tb:2.label Rect: 124, 236, 130, 245 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 338, 141, 345, 150 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination eq:red.label Rect: 183, 93, 196, 102 Destination: 74 Page: Label: 1080 Sequence: 10 Annotations: Annotation: Subtype: Link Contents: Link to named destination QS-2cl.label Rect: 398, 583, 412, 592 Destination: 61 Annotation: Subtype: Link Contents: Link to named destination cite.Bautin Rect: 52, 536, 59, 544 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination lem:0lc.label Rect: 380, 471, 393, 480 Destination: 87 Annotation: Subtype: Link Contents: Link to named destination th:cte.label Rect: 135, 459, 149, 468 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination CopB.label Rect: 168, 459, 181, 468 Destination: 124 Annotation: Subtype: Link Contents: Link to named destination cite.GGJ Rect: 380, 279, 392, 287 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.Cop Rect: 88, 145, 95, 153 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.Cop Rect: 112, 119, 119, 127 Destination: 243 Page: Label: 1081 Sequence: 11 Annotations: Annotation: Subtype: Link Contents: Link to named destination thm-lc-C.label Rect: 68, 595, 75, 604 Destination: 13 Annotation: Subtype: Link Contents: Link to named destination cite.Suo Rect: 195, 572, 207, 580 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination th:recta.label Rect: 189, 535, 203, 544 Destination: 87 Annotation: Subtype: Link Contents: Link to named destination cite.Suo Rect: 112, 512, 124, 520 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination prop:1+1.label Rect: 277, 463, 291, 472 Destination: 67 Annotation: Subtype: Link Contents: Link to named destination th:cte.label Rect: 128, 415, 141, 424 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination eqq1.label Rect: 255, 242, 269, 251 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination eqq2.label Rect: 325, 177, 338, 186 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination prop:1+1.label Rect: 266, 129, 280, 138 Destination: 67 Annotation: Subtype: Link Contents: Link to named destination eqq1.label Rect: 110, 117, 123, 126 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination eqq2.label Rect: 148, 105, 162, 114 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination th:recta.label Rect: 420, 105, 433, 114 Destination: 87 Annotation: Subtype: Link Contents: Link to named destination eqq2.label Rect: 86, 57, 99, 66 Destination: 98 Page: Label: 1082 Sequence: 12 Annotations: Annotation: Subtype: Link Contents: Link to named destination eqq2.label Rect: 207, 607, 221, 616 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination eqq2.label Rect: 131, 536, 145, 545 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination eqq3.label Rect: 164, 461, 177, 470 Destination: 114 Annotation: Subtype: Link Contents: Link to named destination eqq3.label Rect: 400, 449, 413, 458 Destination: 114 Annotation: Subtype: Link Contents: Link to named destination eqq4.label Rect: 167, 350, 180, 359 Destination: 114 Annotation: Subtype: Link Contents: Link to named destination eqq5.label Rect: 53, 202, 66, 211 Destination: 114 Annotation: Subtype: Link Contents: Link to named destination eqq5.label Rect: 238, 190, 252, 199 Destination: 114 Page: Label: 1083 Sequence: 13 Annotations: Annotation: Subtype: Link Contents: Link to named destination th:recta.label Rect: 417, 607, 431, 616 Destination: 87 Annotation: Subtype: Link Contents: Link to named destination pro:ge1.label Rect: 277, 535, 291, 544 Destination: 74 Annotation: Subtype: Link Contents: Link to named destination CopB.label Rect: 128, 488, 141, 497 Destination: 124 Annotation: Subtype: Link Contents: Link to named destination th:recta.label Rect: 171, 392, 185, 401 Destination: 87 Annotation: Subtype: Link Contents: Link to named destination thm-lc-C.label Rect: 142, 368, 150, 377 Destination: 13 Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 208, 344, 214, 353 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination lem:0lc.label Rect: 134, 332, 148, 341 Destination: 87 Annotation: Subtype: Link Contents: Link to named destination CopB.label Rect: 420, 332, 433, 341 Destination: 124 Annotation: Subtype: Link Contents: Link to named destination pro:ge1.label Rect: 116, 320, 129, 329 Destination: 74 Annotation: Subtype: Link Contents: Link to named destination pro:ge1.label Rect: 109, 308, 122, 317 Destination: 74 Annotation: Subtype: Link Contents: Link to named destination tb:2.label Rect: 198, 296, 204, 305 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination th:cte.label Rect: 138, 284, 152, 293 Destination: 98 Annotation: Subtype: Link Contents: Link to named destination pro:ge1.label Rect: 391, 284, 404, 293 Destination: 74 Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 179, 260, 185, 269 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 160, 224, 166, 233 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination tb:2.label Rect: 184, 224, 190, 233 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination tb:1.label Rect: 388, 224, 394, 233 Destination: 25 Page: Label: 1084 Sequence: 14 Annotations: Annotation: Subtype: Link Contents: Link to named destination eq:11.label Rect: 137, 534, 150, 543 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination eq:11.label Rect: 71, 522, 84, 531 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination eq:11.label Rect: 376, 471, 390, 479 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination eq:11.label Rect: 270, 395, 284, 404 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination cite.Cop0 Rect: 241, 348, 248, 356 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination eq:11.label Rect: 123, 335, 136, 344 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination cite.ZZ Rect: 107, 308, 119, 316 Destination: 285 Annotation: Subtype: Link Contents: Link to named destination pro:11.label Rect: 216, 283, 229, 292 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination eq:11.label Rect: 223, 247, 236, 256 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination pro:11.label Rect: 207, 235, 220, 244 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination eq:111.label Rect: 361, 94, 379, 102 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination cite.Gan Rect: 234, 58, 241, 66 Destination: 243 Page: Label: 1085 Sequence: 15 Annotations: Annotation: Subtype: Link Contents: Link to named destination eq:111.label Rect: 196, 451, 214, 460 Destination: 144 Page: Label: 1086 Sequence: 16 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.GasGia Rect: 324, 536, 336, 544 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GasGiac21 Rect: 336, 536, 348, 544 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination eq:111.label Rect: 271, 141, 289, 150 Destination: 144 Annotation: Subtype: Link Contents: Link to named destination eq:111.label Rect: 85, 105, 103, 114 Destination: 144 Page: Label: 1087 Sequence: 17 Annotations: Annotation: Subtype: Link Contents: Link to named destination pro:signe.label Rect: 364, 516, 382, 525 Destination: 159 Annotation: Subtype: Link Contents: Link to named destination pro:signe.label Rect: 393, 310, 411, 319 Destination: 159 Page: Label: 1088 Sequence: 18 Annotations: Annotation: Subtype: Link Contents: Link to named destination eq:div.label Rect: 164, 260, 182, 269 Destination: 163 Page: Label: 1089 Sequence: 19 Annotations: Annotation: Subtype: Link Contents: Link to named destination eq:div.label Rect: 392, 556, 410, 565 Destination: 163 Annotation: Subtype: Link Contents: Link to named destination cite.GasGia Rect: 390, 342, 402, 350 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GasGiac21 Rect: 403, 342, 415, 350 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination eq:m1geb.label Rect: 262, 129, 281, 138 Destination: 179 Page: Label: 1090 Sequence: 20 Annotations: Annotation: Subtype: Link Contents: Link to named destination eq:m1geb.label Rect: 126, 440, 144, 449 Destination: 179 Annotation: Subtype: Link Contents: Link to named destination cite.GGG Rect: 419, 429, 431, 437 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GGG Rect: 183, 255, 195, 263 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-lc-C.label Rect: 287, 133, 295, 142 Destination: 13 Page: Label: 1091 Sequence: 21 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.CLT Rect: 285, 514, 292, 522 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GT Rect: 292, 514, 304, 522 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GT Rect: 307, 365, 319, 373 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination eq:QS6.label Rect: 150, 329, 168, 338 Destination: 196 Annotation: Subtype: Link Contents: Link to named destination eq:QS6.label Rect: 332, 257, 350, 266 Destination: 196 Annotation: Subtype: Link Contents: Link to named destination eq:QS4.label Rect: 401, 222, 414, 231 Destination: 13 Annotation: Subtype: Link Contents: Link to named destination cite.I Rect: 243, 199, 255, 207 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination tb:2.label Rect: 119, 163, 125, 172 Destination: 25 Annotation: Subtype: Link Contents: Link to named destination cite.GGT Rect: 179, 58, 191, 66 Destination: 243 Page: Label: 1092 Sequence: 22 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.GGJ Rect: 105, 560, 117, 568 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.GGJ Rect: 213, 416, 225, 424 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination eq:holp.label Rect: 146, 392, 164, 401 Destination: 208 Annotation: Subtype: Link Contents: Link to named destination eq:holp.label Rect: 336, 230, 355, 239 Destination: 208 Annotation: Subtype: Link Contents: Link to named destination eq:holp.label Rect: 409, 206, 427, 215 Destination: 208 Annotation: Subtype: Link Contents: Link to named destination eq:holp.label Rect: 271, 182, 290, 191 Destination: 208 Annotation: Subtype: Link Contents: Link to named destination eq:holp.label Rect: 361, 146, 379, 155 Destination: 208 Page: Label: 1093 Sequence: 23 Annotations: Annotation: Subtype: Link Contents: Link to named destination thm-ap-D.label Rect: 116, 416, 124, 425 Destination: 218 Annotation: Subtype: Link Contents: Link to named destination thm-ap-E.label Rect: 144, 416, 152, 425 Destination: 236 Annotation: Subtype: Link Contents: Link to named destination cite.Andronov Rect: 63, 381, 69, 389 Destination: 243 Page: Label: 1094 Sequence: 24 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.v Rect: 79, 157, 91, 165 Destination: 285 Page: Label: 1095 Sequence: 25 Annotations: Annotation: Subtype: Link Contents: Link to named destination thm-ap-D.label Rect: 236, 153, 245, 162 Destination: 218 Page: Label: 1096 Sequence: 26 Annotations: Annotation: Subtype: Link Contents: Link to named destination coro.label Rect: 239, 607, 257, 616 Destination: 232 Annotation: Subtype: Link Contents: Link to named destination cite.Andronov Rect: 210, 498, 217, 506 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination cite.CGM Rect: 423, 262, 430, 270 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-ap-D.label Rect: 310, 237, 318, 246 Destination: 218 Page: Label: 1097 Sequence: 27 Annotations: Annotation: Subtype: Link Contents: Link to named destination cite.GGM Rect: 416, 536, 428, 544 Destination: 243 Annotation: Subtype: Link Contents: Link to named destination thm-ap-D.label Rect: 250, 523, 258, 532 Destination: 218 Annotation: Subtype: Link Rect: 67, 418, 432, 426 Annotation: Subtype: Link Rect: 67, 408, 218, 414 Annotation: Subtype: Link Rect: 67, 398, 432, 404 Annotation: Subtype: Link Rect: 67, 388, 432, 394 Annotation: Subtype: Link Rect: 67, 378, 432, 384 Annotation: Subtype: Link Rect: 67, 368, 127, 374 Annotation: Subtype: Link Rect: 67, 358, 432, 364 Annotation: Subtype: Link Rect: 67, 348, 185, 354 Annotation: Subtype: Link Rect: 67, 338, 395, 344 Annotation: Subtype: Link Rect: 67, 328, 432, 334 Annotation: Subtype: Link Rect: 67, 318, 108, 324 Annotation: Subtype: Link Rect: 67, 308, 318, 314 Annotation: Subtype: Link Rect: 67, 298, 373, 304 Annotation: Subtype: Link Rect: 67, 288, 432, 294 Annotation: Subtype: Link Rect: 67, 278, 280, 284 Annotation: Subtype: Link Rect: 67, 268, 432, 274 Annotation: Subtype: Link Rect: 67, 259, 93, 264 Annotation: Subtype: Link Rect: 67, 248, 432, 254 Annotation: Subtype: Link Rect: 67, 238, 219, 244 Annotation: Subtype: Link Rect: 67, 228, 432, 235 Annotation: Subtype: Link Rect: 67, 218, 141, 224 Annotation: Subtype: Link Rect: 67, 208, 432, 214 Annotation: Subtype: Link Rect: 67, 198, 398, 204 Annotation: Subtype: Link Rect: 67, 188, 415, 194 Annotation: Subtype: Link Rect: 67, 178, 432, 184 Annotation: Subtype: Link Rect: 67, 168, 168, 174 Annotation: Subtype: Link Rect: 67, 158, 432, 164 Annotation: Subtype: Link Rect: 67, 148, 227, 154 Annotation: Subtype: Link Rect: 67, 138, 432, 144 Annotation: Subtype: Link Rect: 67, 129, 97, 134 Annotation: Subtype: Link Rect: 67, 118, 432, 124 Annotation: Subtype: Link Rect: 67, 109, 105, 114 Annotation: Subtype: Link Rect: 67, 98, 432, 104 Annotation: Subtype: Link Rect: 67, 86, 432, 96 Annotation: Subtype: Link Rect: 67, 78, 189, 84 Annotation: Subtype: Link Rect: 67, 68, 432, 74 Annotation: Subtype: Link Rect: 67, 58, 184, 64 Page: Label: 1098 Sequence: 28 Annotations: Annotation: Subtype: Link Rect: 67, 608, 432, 614 Annotation: Subtype: Link Rect: 67, 598, 161, 604 Annotation: Subtype: Link Rect: 67, 588, 432, 594 Annotation: Subtype: Link Rect: 67, 579, 97, 584 Annotation: Subtype: Link Rect: 67, 568, 408, 574 Annotation: Subtype: Link Rect: 67, 557, 432, 564 Annotation: Subtype: Link Rect: 67, 548, 185, 554 Checksum: cf175dd7 Type: CRC32 Checksum: 96f0f4fe0959213c30e402766239e137 Type: MD5 Checksum: 4959b7c2457783c4a168bcbb0f6e485dc6960e74 Type: SHA-1 Checksum: a6e61592edd6b97f3c4c0f328e78582b6a82b75bc89151a937e0efeff8761d35 Type: SHA-256