bfe0eb443b3fb3f342f5eeb1f54c9840 saopaujou_a2025m6v19n1p4.pdf 9b81230bc44eda28f3e6d4ea7ce043b3d8e91f7a saopaujou_a2025m6v19n1p4.pdf 3b4b35299b8c47bffa47b832787928b68b12bd859829a88d1db6fa2ff855c096 saopaujou_a2025m6v19n1p4.pdf Title: Cubic planar vector fields with high local cyclicity Subject: São Paulo Journal of Mathematical Sciences, https://doi.org/10.1007/s40863-024-00486-9 Keywords: Center-focus; Cyclicity; Limit cycles; Weak-focus order; Lyapunov quantities Author: Joan Torregrosa Creator: Springer Producer: Acrobat Distiller 10.1.8 (Windows); modified using iText® 5.3.5 ©2000-2012 1T3XT BVBA (SPRINGER SBM; licensed version) CreationDate: Thu Dec 26 02:59:35 2024 CET ModDate: Wed Feb 12 18:08:55 2025 CET Custom Metadata: yes Metadata Stream: yes Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 16 Encrypted: no Page size: 439.37 x 666.142 pts Page rot: 0 File size: 1155805 bytes Optimized: yes PDF version: 1.4 name type encoding emb sub uni object ID 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Date: 2025-02-13 02:52:12 CET RepresentationInformation: saopaujou_a2025m6v19n1p4.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-02-12 18:09:11 CET Size: 1155805 Format: PDF Version: 1.4 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf Profile: Linearized PDF PDFMetadata: Objects: 1761 FreeObjects: 1 IncrementalUpdates: 1 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: false CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseOutlines Language: EN Outlines: Item: Title: Cubic planar vector fields with high local cyclicity Children: Item: Title: Abstract Item: Title: 1 Introduction Item: Title: 2 Preliminaries Item: Title: 3 Proofs of the main results Item: Title: Acknowledgements Item: Title: References Info: Title: Cubic planar vector fields with high local cyclicity Author: Joan Torregrosa Subject: São Paulo Journal of Mathematical Sciences, https://doi.org/10.1007/s40863-024-00486-9 Keywords: Center-focus; Cyclicity; Limit cycles; Weak-focus order; Lyapunov quantities Creator: Springer Producer: Acrobat Distiller 10.1.8 (Windows); modified using iText® 5.3.5 ©2000-2012 1T3XT BVBA (SPRINGER SBM; licensed version) CreationDate: Thu Dec 26 03:29:35 CET 2024 ModDate: Wed Feb 12 18:08:55 CET 2025 ID: 0x5caac2967cc7676f2a84b3608aaae321, 0x12b7bd771b8efa48a3336ef5f2178a72 Filters: FilterPipeline: FlateDecode Images: Image: NisoImageMetadata: FormatName: image/png ImageWidth: 120 ImageHeight: 119 BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Intent: RelativeColorimetric Decode: 0, 255 Name: X Fonts: Type1: Font: BaseFont: TQCMUM+STIXMath-Regular50 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular50 Flags: Symbolic FontBBox: 0, -222, 888, 710 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BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular62 FontSubset: true FirstChar: 22 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular62 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular61 FontSubset: true FirstChar: 22 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular61 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular55 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular55 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular60 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular60 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular65 FontSubset: true FirstChar: 26 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular65 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic56 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic56 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular66 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular66 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular64 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular64 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular63 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular63 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular56 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular56 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular69 FontSubset: true FirstChar: 25 LastChar: 33 FontDescriptor: FontName: 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Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic58 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic58 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular68 FontSubset: true FirstChar: 23 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular68 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular3 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular3 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic57 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic57 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: WDKGKG+STIXMathExtensions-Regular FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: WDKGKG+STIXMathExtensions-Regular Flags: Symbolic FontBBox: 0, -2394, 1163, 959 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular3 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular3 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular4 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular4 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: 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688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular5 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular5 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular73 FontSubset: true FirstChar: 25 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular73 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular58 FontSubset: true FirstChar: 28 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular58 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic59 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic59 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular78 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular78 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular59 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular59 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic4 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic4 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular74 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular74 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TWBOUM+STIXMath-Italic FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular60 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular60 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular75 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: 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ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic60 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic60 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular79 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular79 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular6 FontSubset: true FirstChar: 25 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular6 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular80 FontSubset: true FirstChar: 21 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular80 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular6 FontSubset: true FirstChar: 26 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular6 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXMath-Regular62 FontSubset: true FirstChar: 28 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular62 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular81 FontSubset: true FirstChar: 22 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular81 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: 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888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TWBOUM+STIXMath-Italic3 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic3 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular9 FontSubset: true FirstChar: 21 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular9 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: MyriadPro-BoldSemiCn FirstChar: 0 LastChar: 255 FontDescriptor: FontName: MyriadPro-BoldSemiCn Flags: Nonsymbolic FontBBox: -133, -250, 1161, 894 FontFile3: true Encoding: WinAnsiEncoding ToUnicode: true Font: BaseFont: QBAFJQ+STIX-Bold FontSubset: true FirstChar: 0 LastChar: 255 FontDescriptor: FontName: QBAFJQ+STIX-Bold Flags: Serif, Nonsymbolic FontBBox: -998, -552, 2000, 1055 FontFile3: true Encoding: WinAnsiEncoding ToUnicode: true Font: BaseFont: WDKGKG+STIXMathExtensions-Regular2 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: WDKGKG+STIXMathExtensions-Regular2 Flags: Symbolic FontBBox: 0, -2394, 1163, 959 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular7 FontSubset: true FirstChar: 22 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular7 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular8 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular8 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: QCJLUS+STIXGeneral-Italic61 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: QCJLUS+STIXGeneral-Italic61 Flags: Symbolic, SmallCap FontBBox: -6, -209, 606, 653 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: QCJLUS+STIXGeneral-Italic62 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: QCJLUS+STIXGeneral-Italic62 Flags: Symbolic, SmallCap FontBBox: -6, -209, 606, 653 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: QCJLUS+STIXGeneral-Regular84 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: QCJLUS+STIXGeneral-Regular84 Flags: Symbolic, AllCap FontBBox: 0, 0, 460, 676 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular8 FontSubset: true FirstChar: 23 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular8 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TWBOUM+STIXMath-Italic2 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic2 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular7 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular7 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic5 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic5 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic6 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic6 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular9 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular9 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular12 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular12 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular10 FontSubset: true FirstChar: 26 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular10 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TWBOUM+STIXMath-Italic4 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic4 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular10 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular10 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TWBOUM+STIXMath-Italic5 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic5 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic7 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic7 Flags: Symbolic FontBBox: -147, 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true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic8 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: MyriadPro-SemiboldSemiCn FirstChar: 0 LastChar: 255 FontDescriptor: FontName: MyriadPro-SemiboldSemiCn Flags: Nonsymbolic FontBBox: -131, -250, 1115, 886 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: MyriadPro-Bold FirstChar: 0 LastChar: 255 FontDescriptor: FontName: MyriadPro-Bold Flags: Nonsymbolic FontBBox: -163, -250, 1256, 989 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TWBOUM+STIXMath-Italic7 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic7 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: ZVGEFA+STIX-Regular FontSubset: true FirstChar: 26 LastChar: 246 FontDescriptor: FontName: ZVGEFA+STIX-Regular Flags: Serif, Nonsymbolic FontBBox: -970, -486, 2208, 1023 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXMath-Regular12 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular12 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic9 FontSubset: true FirstChar: 27 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic9 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular13 FontSubset: true FirstChar: 26 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular13 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic11 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic11 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: WDKGKG+STIXMathExtensions-Regular3 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: WDKGKG+STIXMathExtensions-Regular3 Flags: Symbolic FontBBox: 0, -2394, 1163, 959 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TWBOUM+STIXMath-Italic9 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic9 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular14 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular14 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: QKHOUB+Wingdings-Regular FontSubset: true FirstChar: 0 LastChar: 255 FontDescriptor: FontName: QKHOUB+Wingdings-Regular Flags: Nonsymbolic FontBBox: 0, -103, 1359, 439 FontFile3: true Encoding: WinAnsiEncoding ToUnicode: true Font: BaseFont: HEXPIK+STIXMathCalligraphy-Regular FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: HEXPIK+STIXMathCalligraphy-Regular Flags: Symbolic FontBBox: 0, -156, 637, 662 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Italic10 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic10 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular14 FontSubset: true FirstChar: 26 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular14 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TQCMUM+STIXGeneral-Regular15 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular15 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic12 FontSubset: true FirstChar: 28 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic12 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TWBOUM+STIXMath-Italic11 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic11 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular16 FontSubset: true FirstChar: 28 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular16 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true ToUnicode: true Font: BaseFont: TWBOUM+STIXMath-Italic10 FontSubset: true FirstChar: 29 LastChar: 33 FontDescriptor: FontName: TWBOUM+STIXMath-Italic10 Flags: Symbolic FontBBox: 0, -187, 661, 674 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXMath-Regular15 FontSubset: true FirstChar: 28 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXMath-Regular15 Flags: Symbolic FontBBox: 0, -222, 888, 710 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true 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EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic17 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic17 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Italic18 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Italic18 Flags: Symbolic FontBBox: -147, -207, 906, 683 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular19 FontSubset: true FirstChar: 31 LastChar: 33 FontDescriptor: FontName: TQCMUM+STIXGeneral-Regular19 Flags: Symbolic, SmallCap FontBBox: 0, -122, 485, 688 FontFile3: true EncodingDictionary: BaseEncoding: WinAnsiEncoding Differences: true Font: BaseFont: TQCMUM+STIXGeneral-Regular18 FontSubset: true FirstChar: 30 LastChar: 33 FontDescriptor: 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Lyapunov quantities False application/pdf https://doi.org/10.1007/s40863-024-00486-9 Springer International Publishing São Paulo Journal of Mathematical Sciences, https://doi.org/10.1007/s40863-024-00486-9 Center-focus Cyclicity Limit cycles Weak-focus order Lyapunov quantities Cubic planar vector fields with high local cyclicity Joan Torregrosa 10.1007/s40863-024-00486-9 2010-04-23 true springer.com springerlink.com https://doi.org/10.1007/s40863-024-00486-9 10.1007/s40863-024-00486-9 2316-9028 journal São Paulo Journal of Mathematical Sciences The Author(s) 2010-04-23 true 10.1007/s40863-024-00486-9 noindex springer.com springerlink.com VoR uuid:575be6e6-3225-45a1-8b7a-0d15ec038b47 uuid:fecaaa5b-34f4-46bf-9692-36e592f9bfbc default 1 converted uuid:575be6e6-3225-45a1-8b7a-0d15ec038b47 converted to PDF/A-2b pdfToolbox 2024-12-26T07:30:35+05:30 converted uuid:85ef42b7-b0c7-48c2-be8e-8233c0a20cdc converted to PDF/A-2b pdfToolbox 2024-12-26T07:31:20+05:30 2 B Joan Torregrosa 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