880e947f480f22414a3911a3470d294f axi_a2023m8v12n8p756.pdf baf832d3cfefa114afb1dc72746fd4abf7d302cf axi_a2023m8v12n8p756.pdf c370e3182dbc550e11049880153ca1a8aa1efb601dab6bd8f82f99ee4c20b575 axi_a2023m8v12n8p756.pdf Title: Phase Portraits of Families VII and VIII of the Quadratic Systems Subject: The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications. These systems can be classified into ten classes. Here, we provide all topologically different phase portraits in the Poincaré disc of two of these classes. Keywords: quadratic vector fields; quadratic systems; phase portraits Author: Laurent Cairó and Jaume Llibre Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Tue Aug 22 04:22:49 2023 CEST ModDate: Tue Aug 22 04:25:12 2023 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 18 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 790561 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- HLYYFJ+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 PNGVUD+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 TFIGPS+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 PYDYKJ+CMR10 Type 1 Builtin yes yes no 23 0 QEWLTU+CMMI10 Type 1 Builtin yes yes no 27 0 GDTBFJ+CMSY10 Type 1 Builtin yes yes no 31 0 XVOAMZ+MSBM10 Type 1 Builtin yes yes no 35 0 SKSVGJ+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 53 0 HDWKCG+CMEX10 Type 1 Builtin yes yes no 78 0 ZZVEAX+URWPalladioL-BoldItal Type 1 Custom yes yes no 85 0 ZOVVDX+CMCSC10 Type 1 Custom yes yes no 94 0 PYDYKJ+CMR10 Type 1 Custom yes yes no 99 0 QEWLTU+CMMI10 Type 1 Custom yes yes yes 102 0 YYPVCU+CMR7 Type 1 Custom yes yes no 106 0 GDTBFJ+CMSY10 Type 1 Custom yes yes yes 111 0 HDWKCG+CMEX10 Type 1 Custom yes yes yes 115 0 PCUKZC+CMSY7 Type 1 Custom yes yes no 119 0 OBGSCU+ArialMT Type 1C Custom yes yes no 124 0 ZOVVDX+CMCSC10 Type 1 Custom yes yes no 133 0 PYDYKJ+CMR10 Type 1 Custom yes yes no 135 0 QEWLTU+CMMI10 Type 1 Custom yes yes yes 137 0 YYPVCU+CMR7 Type 1 Custom yes yes no 140 0 GDTBFJ+CMSY10 Type 1 Custom yes yes yes 142 0 HDWKCG+CMEX10 Type 1 Custom yes yes yes 145 0 PCUKZC+CMSY7 Type 1 Custom yes yes no 148 0 OBGSCU+ArialMT Type 1C Custom yes yes no 150 0 DWMJYR+CMBX10 Type 1 Custom yes yes no 162 0 ZOVVDX+CMCSC10 Type 1 Custom yes yes no 167 0 PYDYKJ+CMR10 Type 1 Custom yes yes no 169 0 UMPZYI+CMTI10 Type 1 Custom yes yes no 171 0 QEWLTU+CMMI10 Type 1 Custom yes yes yes 176 0 YYPVCU+CMR7 Type 1 Custom yes yes no 179 0 GDTBFJ+CMSY10 Type 1 Custom yes yes yes 181 0 PCUKZC+CMSY7 Type 1 Custom yes yes no 184 0 OBGSCU+ArialMT Type 1C Custom yes yes no 186 0 KMUTNG+PazoMath Type 1 Builtin yes yes no 193 0 JUCXNO+ArialMT Type 1C WinAnsi yes yes no 203 0 DAADZB+ArialMT Type 1C WinAnsi yes yes no 212 0 FMMSON+ArialMT Type 1C WinAnsi yes yes no 226 0 EVFBMN+ArialMT Type 1C Custom yes yes no 254 0 IYOJJU+ArialMT Type 1C WinAnsi yes yes no 271 0 HMZZCF+ArialMT Type 1C WinAnsi yes yes no 280 0 FMMSON+ArialMT Type 1C WinAnsi yes yes no 297 0 EVFBMN+ArialMT Type 1C Custom yes yes no 328 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2024-03-08 02:36:48 CET RepresentationInformation: axi_a2023m8v12n8p756.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2024-03-07 17:36:31 CET Size: 790561 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 579 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction and Statement of the Main Results Destination: section.1 Item: Title: Preliminary Definitions Destination: section.2 Children: Item: Title: Equilibrium Points Destination: subsection.2.1 Item: Title: Poincaré Compactification Destination: subsection.2.2 Item: Title: Phase Portraits on the Poincaré Disc Destination: subsection.2.3 Item: Title: Proof of Statement (a) of Theorem 1 Destination: section.3 Children: Item: Title: Finite Equilibrium Points Destination: subsection.3.1 Item: Title: The Infinite Equilibrium Points in Chart U1 Destination: subsection.3.2 Item: Title: The Infinite Equilibrium Point at the Origin of Chart U2 Destination: subsection.3.3 Item: Title: The Global Phase Portraits Destination: subsection.3.4 Item: Title: Proof of Statement (b) Theorem 1 Destination: section.4 Children: Item: Title: Finite Equilibrium Points Destination: subsection.4.1 Item: Title: The Infinite Equilibrium Points in Chart U1 Destination: subsection.4.2 Item: Title: The Infinite Equilibrium Point at the Origin of Chart U2 Destination: subsection.4.3 Item: Title: The Global Phase Portraits Destination: subsection.4.4 Item: Title: References Destination: section.5 Info: Title: Phase Portraits of Families VII and VIII of the Quadratic Systems Author: Laurent Cairó and Jaume Llibre Subject: The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications. These systems can be classified into ten classes. Here, we provide all topologically different phase portraits in the Poincaré disc of two of these classes. 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