0d40b14688dda95eb50953712776d6a6 axioms_12_00342.pdf e98c145b913ee07ae283c605587a50ba1d4ebbcb axioms_12_00342.pdf 4432a151efe90db400ce6993d79a290f673b1b65e05136f07f70cd994a075b98 axioms_12_00342.pdf Title: Limit Cycles of Polynomially Integrable Piecewise Differential Systems Subject: In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals. Keywords: algebraic limit cycle; piecewise differential system; polynomial integrable systems Author: Belén García, Jaume Llibre, Jesús S. Pérez del Río and Set Pérez-González Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Fri Mar 31 10:50:40 2023 CEST ModDate: Fri Mar 31 10:59:04 2023 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 19 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 407240 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- WHNQTS+CMEX10 Type 1 Builtin yes yes no 10 0 VWHMBY+URWPalladioL-Bold Type 1 Custom yes yes no 14 0 JBHUOS+URWPalladioL-Roma Type 1 Custom yes yes no 19 0 VQDMVZ+URWPalladioL-Ital Type 1 Custom yes yes no 23 0 GIGFZE+CMR10 Type 1 Builtin yes yes no 27 0 OZNPIL+CMSY10 Type 1 Builtin yes yes no 31 0 SVPXIN+MSBM10 Type 1 Builtin yes yes no 35 0 SKSVGJ+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 53 0 FWGKHK+PazoMath-Italic Type 1 Builtin yes yes no 78 0 VUABVQ+CMMI10 Type 1 Builtin yes yes no 82 0 DHITNT+PazoMath Type 1 Builtin yes yes no 86 0 PXNXHA+ArialMT TrueType WinAnsi yes yes yes 168 0 YTWVXP+MathematicaSans TrueType WinAnsi yes yes yes 172 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-06-23 02:26:35 CEST RepresentationInformation: axioms_12_00342.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-06-21 01:34:32 CEST Size: 407240 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 397 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: Proof of Theorem 1 Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Item: Title: Proof of Theorem 2 Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Examples Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Discussion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Info: Title: Limit Cycles of Polynomially Integrable Piecewise Differential Systems Author: Belén García, Jaume Llibre, Jesús S. Pérez del Río and Set Pérez-González Subject: In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals. Keywords: algebraic limit cycle; piecewise differential system; polynomial integrable systems Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Fri Mar 31 10:50:40 CEST 2023 ModDate: Fri Mar 31 10:59:04 CEST 2023 ID: 0xeba02a022d1e551f6685c26409c0b026, 0xeba02a022d1e551f6685c26409c0b026 Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: VUABVQ+CMMI10 FontSubset: true FirstChar: 60 LastChar: 96 FontDescriptor: FontName: VUABVQ+CMMI10 Flags: Symbolic FontBBox: -32, -250, 1048, 750 FontFile: true Font: BaseFont: SVPXIN+MSBM10 FontSubset: true FirstChar: 78 LastChar: 90 FontDescriptor: FontName: SVPXIN+MSBM10 Flags: Symbolic FontBBox: -55, -420, 2343, 920 FontFile: true Font: BaseFont: JBHUOS+URWPalladioL-Roma FontSubset: true FirstChar: 1 LastChar: 243 FontDescriptor: FontName: JBHUOS+URWPalladioL-Roma Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: DHITNT+PazoMath FontSubset: true FirstChar: 83 LastChar: 229 FontDescriptor: FontName: DHITNT+PazoMath Flags: Symbolic FontBBox: -40, -283, 878, 946 FontFile: true Font: BaseFont: VQDMVZ+URWPalladioL-Ital FontSubset: true FirstChar: 2 LastChar: 150 FontDescriptor: FontName: VQDMVZ+URWPalladioL-Ital Flags: Symbolic FontBBox: -170, -305, 1010, 941 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: WHNQTS+CMEX10 FontSubset: true FirstChar: 0 LastChar: 67 FontDescriptor: FontName: WHNQTS+CMEX10 Flags: Symbolic FontBBox: -24, -2960, 1454, 772 FontFile: true Font: BaseFont: GIGFZE+CMR10 FontSubset: true FirstChar: 40 LastChar: 61 FontDescriptor: FontName: GIGFZE+CMR10 Flags: Symbolic FontBBox: -40, -250, 1009, 750 FontFile: true Font: BaseFont: VWHMBY+URWPalladioL-Bold FontSubset: true FirstChar: 3 LastChar: 250 FontDescriptor: FontName: VWHMBY+URWPalladioL-Bold Flags: Symbolic FontBBox: -152, -301, 1000, 935 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: FWGKHK+PazoMath-Italic FontSubset: true FirstChar: 97 LastChar: 119 FontDescriptor: FontName: FWGKHK+PazoMath-Italic Flags: Symbolic FontBBox: -70, -277, 902, 733 FontFile: true Font: BaseFont: OZNPIL+CMSY10 FontSubset: true FirstChar: 0 LastChar: 112 FontDescriptor: FontName: OZNPIL+CMSY10 Flags: Symbolic FontBBox: -29, -960, 1116, 775 FontFile: true Pages: Page: Sequence: 1 Annotations: Annotation: Subtype: Link Rect: 34, 279, 152, 288 Annotation: Subtype: Link Rect: 34, 269, 86, 276 Annotation: Subtype: Link Rect: 34, 164, 96, 186 Annotation: Subtype: Link Rect: 126, 90, 154, 99 Annotation: Subtype: Link Rect: 34, 78, 147, 87 Annotation: Subtype: Link Rect: 34, 756, 155, 792 Annotation: Subtype: Link Rect: 515, 756, 560, 792 Annotation: Subtype: Link Rect: 189, 661, 200, 674 Annotation: Subtype: Link Rect: 436, 661, 447, 674 Annotation: Subtype: Link Rect: 284, 263, 291, 272 ActionDest: 158 Annotation: Subtype: Link Rect: 351, 251, 358, 259 ActionDest: 158 Annotation: Subtype: Link Rect: 342, 238, 349, 247 ActionDest: 158 Annotation: Subtype: Link Rect: 350, 238, 357, 247 ActionDest: 158 Annotation: Subtype: Link Rect: 434, 238, 441, 247 ActionDest: 176 Annotation: Subtype: Link Rect: 209, 148, 216, 159 ActionDest: 5 Annotation: Subtype: Link Rect: 244, 148, 251, 159 ActionDest: 5 Annotation: Subtype: Link Rect: 369, 137, 376, 146 ActionDest: 176 Annotation: Subtype: Link Rect: 263, 85, 270, 97 ActionDest: 5 Annotation: Subtype: Link Rect: 297, 85, 304, 97 ActionDest: 5 Annotation: Subtype: Link Rect: 311, 87, 318, 96 ActionDest: 176 Annotation: Subtype: Link Rect: 109, 17, 259, 28 Annotation: Subtype: Link Rect: 411, 17, 560, 28 Annotation: Subtype: Link Rect: 34, 353, 87, 372 Page: Sequence: 2 Annotations: Annotation: Subtype: Link Rect: 348, 736, 355, 744 ActionDest: 176 Annotation: Subtype: Link Rect: 517, 733, 524, 745 ActionDest: 5 Annotation: Subtype: Link Rect: 550, 733, 557, 745 ActionDest: 5 Annotation: Subtype: Link Rect: 495, 673, 502, 682 ActionDest: 176 Annotation: Subtype: Link Rect: 241, 314, 248, 325 ActionDest: 5 Annotation: Subtype: Link Rect: 273, 314, 280, 325 ActionDest: 5 Annotation: Subtype: Link Rect: 379, 277, 386, 288 ActionDest: 5 Annotation: Subtype: Link Rect: 410, 277, 417, 288 ActionDest: 5 Annotation: Subtype: Link Rect: 426, 226, 433, 238 ActionDest: 75 Annotation: Subtype: Link Rect: 553, 226, 560, 238 ActionDest: 72 Annotation: Subtype: Link Rect: 553, 214, 560, 226 ActionDest: 105 Annotation: Subtype: Link Rect: 284, 201, 291, 213 ActionDest: 72 Annotation: Subtype: Link Rect: 463, 201, 470, 213 ActionDest: 72 Annotation: Subtype: Link Rect: 552, 201, 559, 213 ActionDest: 142 Annotation: Subtype: Link Rect: 301, 189, 308, 201 ActionDest: 5 Annotation: Subtype: Link Rect: 336, 189, 343, 201 ActionDest: 5 Annotation: Subtype: Link Rect: 201, 166, 208, 175 ActionDest: 176 Annotation: Subtype: Link Rect: 505, 103, 517, 113 ActionDest: 176 Annotation: Subtype: Link Rect: 521, 91, 533, 100 ActionDest: 176 Page: Sequence: 3 Annotations: Annotation: Subtype: Link Rect: 525, 736, 537, 744 ActionDest: 176 Annotation: Subtype: Link Rect: 258, 697, 265, 710 ActionDest: 72 Annotation: Subtype: Link Rect: 309, 682, 316, 694 ActionDest: 72 Annotation: Subtype: Link Rect: 307, 563, 314, 575 ActionDest: 75 Annotation: Subtype: Link Rect: 246, 364, 253, 375 ActionDest: 75 Annotation: Subtype: Link Rect: 377, 78, 384, 90 ActionDest: 72 Page: Sequence: 4 Annotations: Annotation: Subtype: Link Rect: 288, 301, 295, 312 ActionDest: 90 Annotation: Subtype: Link Rect: 523, 301, 530, 312 ActionDest: 90 Annotation: Subtype: Link Rect: 204, 226, 216, 238 ActionDest: 90 Annotation: Subtype: Link Rect: 507, 226, 514, 238 ActionDest: 90 Annotation: Subtype: Link Rect: 258, 202, 265, 213 ActionDest: 90 Annotation: Subtype: Link Rect: 268, 189, 275, 201 ActionDest: 90 Annotation: Subtype: Link Rect: 268, 152, 275, 163 ActionDest: 90 Annotation: Subtype: Link Rect: 269, 103, 276, 114 ActionDest: 90 Annotation: Subtype: Link Rect: 248, 71, 255, 81 ActionDest: 72 Page: Sequence: 5 Annotations: Annotation: Subtype: Link Rect: 420, 733, 427, 745 ActionDest: 72 Annotation: Subtype: Link Rect: 202, 592, 208, 603 ActionDest: 72 Annotation: Subtype: Link Rect: 441, 576, 453, 588 ActionDest: 93 Annotation: Subtype: Link Rect: 347, 525, 359, 536 ActionDest: 93 Annotation: Subtype: Link Rect: 218, 409, 225, 420 ActionDest: 72 Annotation: Subtype: Link Rect: 213, 292, 225, 303 ActionDest: 93 Annotation: Subtype: Link Rect: 222, 248, 233, 259 ActionDest: 93 Annotation: Subtype: Link Rect: 442, 247, 449, 259 ActionDest: 90 Annotation: Subtype: Link Rect: 203, 149, 215, 161 ActionDest: 93 Annotation: Subtype: Link Rect: 354, 136, 360, 148 ActionDest: 75 Annotation: Subtype: Link Rect: 473, 137, 485, 148 ActionDest: 93 Page: Sequence: 6 Annotations: Annotation: Subtype: Link Rect: 219, 608, 226, 620 ActionDest: 75 Annotation: Subtype: Link Rect: 300, 608, 312, 620 ActionDest: 93 Annotation: Subtype: Link Rect: 246, 439, 258, 450 ActionDest: 96 Annotation: Subtype: Link Rect: 268, 439, 280, 450 ActionDest: 96 Annotation: Subtype: Link Rect: 306, 439, 318, 450 ActionDest: 96 Annotation: Subtype: Link Rect: 215, 385, 227, 396 ActionDest: 96 Annotation: Subtype: Link Rect: 334, 346, 346, 357 ActionDest: 93 Annotation: Subtype: Link Rect: 241, 300, 253, 311 ActionDest: 96 Annotation: Subtype: Link Rect: 261, 300, 273, 311 ActionDest: 96 Annotation: Subtype: Link Rect: 282, 300, 293, 311 ActionDest: 96 Annotation: Subtype: Link Rect: 302, 300, 313, 311 ActionDest: 96 Annotation: Subtype: Link Rect: 367, 288, 374, 299 ActionDest: 72 Annotation: Subtype: Link Rect: 193, 275, 205, 286 ActionDest: 93 Annotation: Subtype: Link Rect: 232, 275, 243, 286 ActionDest: 93 Page: Sequence: 7 Annotations: Annotation: Subtype: Link Rect: 268, 436, 280, 447 ActionDest: 96 Annotation: Subtype: Link Rect: 354, 323, 361, 335 ActionDest: 72 Annotation: Subtype: Link Rect: 192, 296, 204, 307 ActionDest: 93 Annotation: Subtype: Link Rect: 239, 264, 246, 278 ActionDest: 75 Annotation: Subtype: Link Rect: 383, 265, 395, 276 ActionDest: 93 Annotation: Subtype: Link Rect: 281, 189, 288, 201 ActionDest: 90 Annotation: Subtype: Link Rect: 268, 111, 275, 123 ActionDest: 75 Page: Sequence: 8 Annotations: Annotation: Subtype: Link Rect: 420, 690, 427, 701 ActionDest: 90 Annotation: Subtype: Link Rect: 290, 631, 302, 642 ActionDest: 99 Annotation: Subtype: Link Rect: 446, 615, 453, 627 ActionDest: 72 Annotation: Subtype: Link Rect: 483, 492, 495, 504 ActionDest: 102 Annotation: Subtype: Link Rect: 351, 433, 358, 445 ActionDest: 72 Annotation: Subtype: Link Rect: 532, 409, 544, 420 ActionDest: 93 Annotation: Subtype: Link Rect: 399, 254, 411, 265 ActionDest: 102 Annotation: Subtype: Link Rect: 287, 114, 299, 125 ActionDest: 102 Page: Sequence: 9 Annotations: Annotation: Subtype: Link Rect: 336, 483, 347, 494 ActionDest: 102 Annotation: Subtype: Link Rect: 207, 459, 213, 469 ActionDest: 72 Annotation: Subtype: Link Rect: 385, 429, 397, 441 ActionDest: 102 Annotation: Subtype: Link Rect: 440, 429, 447, 441 ActionDest: 72 Annotation: Subtype: Link Rect: 273, 138, 280, 150 ActionDest: 72 Annotation: Subtype: Link Rect: 553, 138, 560, 150 ActionDest: 72 Annotation: Subtype: Link Rect: 258, 103, 265, 115 ActionDest: 72 Annotation: Subtype: Link Rect: 230, 88, 237, 100 ActionDest: 72 Annotation: Subtype: Link Rect: 550, 88, 557, 100 ActionDest: 5 Annotation: Subtype: Link Rect: 187, 76, 194, 87 ActionDest: 5 Annotation: Subtype: Link Rect: 337, 62, 344, 74 ActionDest: 72 Annotation: Subtype: Link Rect: 510, 65, 522, 74 ActionDest: 176 Page: Sequence: 10 Annotations: Annotation: Subtype: Link Rect: 216, 622, 228, 631 ActionDest: 176 Annotation: Subtype: Link Rect: 550, 620, 557, 632 ActionDest: 5 Annotation: Subtype: Link Rect: 188, 608, 195, 619 ActionDest: 5 Annotation: Subtype: Link Rect: 274, 608, 286, 619 ActionDest: 108 Annotation: Subtype: Link Rect: 313, 608, 325, 619 ActionDest: 108 Annotation: Subtype: Link Rect: 508, 570, 520, 581 ActionDest: 108 Annotation: Subtype: Link Rect: 545, 570, 557, 581 ActionDest: 108 Annotation: Subtype: Link Rect: 234, 557, 241, 569 ActionDest: 72 Annotation: Subtype: Link Rect: 335, 489, 347, 500 ActionDest: 108 Annotation: Subtype: Link Rect: 239, 378, 246, 390 ActionDest: 72 Annotation: Subtype: Link Rect: 292, 366, 304, 377 ActionDest: 108 Annotation: Subtype: Link Rect: 207, 353, 213, 365 ActionDest: 72 Annotation: Subtype: Link Rect: 239, 354, 251, 365 ActionDest: 108 Annotation: Subtype: Link Rect: 287, 341, 299, 352 ActionDest: 108 Annotation: Subtype: Link Rect: 326, 341, 333, 352 ActionDest: 72 Annotation: Subtype: Link Rect: 391, 340, 398, 352 ActionDest: 72 Annotation: Subtype: Link Rect: 363, 315, 370, 327 ActionDest: 72 Annotation: Subtype: Link Rect: 226, 178, 238, 190 ActionDest: 108 Page: Sequence: 11 Annotations: Annotation: Subtype: Link Rect: 225, 687, 236, 698 ActionDest: 108 Annotation: Subtype: Link Rect: 435, 674, 442, 685 ActionDest: 72 Annotation: Subtype: Link Rect: 222, 490, 234, 501 ActionDest: 111 Annotation: Subtype: Link Rect: 261, 490, 273, 501 ActionDest: 111 Annotation: Subtype: Link Rect: 249, 478, 261, 489 ActionDest: 108 Annotation: Subtype: Link Rect: 444, 477, 451, 490 ActionDest: 108 Annotation: Subtype: Link Rect: 280, 453, 292, 464 ActionDest: 108 Annotation: Subtype: Link Rect: 222, 360, 234, 371 ActionDest: 108 Annotation: Subtype: Link Rect: 402, 266, 409, 278 ActionDest: 108 Page: Sequence: 12 Annotations: Annotation: Subtype: Link Rect: 507, 720, 514, 732 ActionDest: 72 Annotation: Subtype: Link Rect: 242, 670, 249, 682 ActionDest: 115 Annotation: Subtype: Link Rect: 432, 479, 439, 491 ActionDest: 72 Annotation: Subtype: Link Rect: 387, 455, 399, 466 ActionDest: 108 Annotation: Subtype: Link Rect: 426, 455, 438, 466 ActionDest: 108 Annotation: Subtype: Link Rect: 512, 382, 524, 391 ActionDest: 176 Annotation: Subtype: Link Rect: 473, 342, 480, 354 ActionDest: 111 Annotation: Subtype: Link Rect: 533, 317, 540, 329 ActionDest: 115 Page: Sequence: 13 Annotations: Annotation: Subtype: Link Rect: 216, 540, 228, 552 ActionDest: 127 Annotation: Subtype: Link Rect: 306, 528, 318, 539 ActionDest: 127 Annotation: Subtype: Link Rect: 217, 485, 229, 496 ActionDest: 127 Annotation: Subtype: Link Rect: 511, 332, 523, 344 ActionDest: 127 Annotation: Subtype: Link Rect: 347, 226, 359, 237 ActionDest: 127 Annotation: Subtype: Link Rect: 259, 123, 271, 135 ActionDest: 127 Page: Sequence: 14 Annotations: Annotation: Subtype: Link Rect: 245, 614, 252, 626 ActionDest: 130 Annotation: Subtype: Link Rect: 401, 406, 407, 421 ActionDest: 115 Annotation: Subtype: Link Rect: 248, 388, 255, 397 ActionDest: 72 Annotation: Subtype: Link Rect: 400, 385, 407, 397 ActionDest: 111 Annotation: Subtype: Link Rect: 553, 385, 560, 397 ActionDest: 72 Annotation: Subtype: Link Rect: 272, 373, 284, 384 ActionDest: 108 Annotation: Subtype: Link Rect: 312, 373, 324, 384 ActionDest: 108 Annotation: Subtype: Link Rect: 209, 360, 216, 372 ActionDest: 111 Annotation: Subtype: Link Rect: 450, 361, 462, 372 ActionDest: 108 Annotation: Subtype: Link Rect: 488, 361, 500, 372 ActionDest: 108 Annotation: Subtype: Link Rect: 244, 345, 256, 356 ActionDest: 108 Annotation: Subtype: Link Rect: 285, 345, 297, 356 ActionDest: 108 Annotation: Subtype: Link Rect: 540, 344, 547, 356 ActionDest: 108 Annotation: Subtype: Link Rect: 203, 332, 215, 344 ActionDest: 108 Annotation: Subtype: Link Rect: 355, 332, 367, 344 ActionDest: 108 Annotation: Subtype: Link Rect: 206, 320, 218, 331 ActionDest: 108 Annotation: Subtype: Link Rect: 246, 320, 258, 331 ActionDest: 108 Annotation: Subtype: Link Rect: 303, 260, 310, 272 ActionDest: 111 Annotation: Subtype: Link Rect: 464, 223, 476, 234 ActionDest: 108 Annotation: Subtype: Link Rect: 505, 223, 517, 234 ActionDest: 108 Annotation: Subtype: Link Rect: 260, 195, 272, 206 ActionDest: 108 Annotation: Subtype: Link Rect: 431, 194, 438, 206 ActionDest: 108 Annotation: Subtype: Link Rect: 479, 195, 490, 206 ActionDest: 108 Annotation: Subtype: Link Rect: 356, 178, 368, 189 ActionDest: 108 Annotation: Subtype: Link Rect: 222, 160, 234, 171 ActionDest: 108 Annotation: Subtype: Link Rect: 261, 160, 273, 171 ActionDest: 108 Page: Sequence: 15 Annotations: Annotation: Subtype: Link Rect: 222, 447, 229, 459 ActionDest: 115 Annotation: Subtype: Link Rect: 416, 370, 423, 382 ActionDest: 115 Annotation: Subtype: Link Rect: 553, 307, 560, 319 ActionDest: 115 Annotation: Subtype: Link Rect: 238, 269, 245, 281 ActionDest: 72 Annotation: Subtype: Link Rect: 494, 130, 501, 144 ActionDest: 142 Page: Sequence: 16 Annotations: Annotation: Subtype: Link Rect: 260, 733, 271, 745 ActionDest: 108 Annotation: Subtype: Link Rect: 460, 733, 467, 745 ActionDest: 108 Annotation: Subtype: Link Rect: 519, 733, 531, 745 ActionDest: 108 Annotation: Subtype: Link Rect: 232, 720, 244, 731 ActionDest: 108 Annotation: Subtype: Link Rect: 221, 706, 233, 717 ActionDest: 108 Annotation: Subtype: Link Rect: 259, 706, 271, 717 ActionDest: 108 Annotation: Subtype: Link Rect: 448, 603, 460, 615 ActionDest: 108 Annotation: Subtype: Link Rect: 486, 603, 498, 615 ActionDest: 108 Annotation: Subtype: Link Rect: 418, 578, 425, 590 ActionDest: 72 Annotation: Subtype: Link Rect: 475, 339, 482, 350 ActionDest: 72 Annotation: Subtype: Link Rect: 225, 190, 237, 201 ActionDest: 142 Annotation: Subtype: Link Rect: 406, 189, 413, 201 ActionDest: 72 Annotation: Subtype: Link Rect: 187, 177, 199, 188 ActionDest: 142 Annotation: Subtype: Link Rect: 224, 139, 235, 151 ActionDest: 142 Annotation: Subtype: Link Rect: 397, 139, 404, 151 ActionDest: 72 Annotation: Subtype: Link Rect: 228, 127, 240, 138 ActionDest: 142 Page: Sequence: 17 Annotations: Annotation: Subtype: Link Rect: 218, 486, 225, 498 ActionDest: 151 Page: Sequence: 18 Annotations: Annotation: Subtype: Link Rect: 217, 650, 223, 662 ActionDest: 158 Page: Sequence: 19 Annotations: Annotation: Subtype: Link Rect: 326, 710, 364, 721 Annotation: Subtype: Link Rect: 95, 688, 132, 698 Annotation: Subtype: Link Rect: 202, 665, 240, 675 Annotation: Subtype: Link Rect: 135, 642, 173, 652 Annotation: Subtype: Link Rect: 220, 618, 258, 629 Annotation: Subtype: Link Rect: 146, 595, 183, 606 Annotation: Subtype: Link Rect: 95, 550, 132, 560 Annotation: Subtype: Link Rect: 184, 527, 221, 537 Checksum: bea7ee42 Type: CRC32 Checksum: 0d40b14688dda95eb50953712776d6a6 Type: MD5 Checksum: e98c145b913ee07ae283c605587a50ba1d4ebbcb Type: SHA-1