198103e10b79e792a31282801c51e350 s12215-025-01256-y.pdf fd8fb106e71e048ea867a120c77cccb25bc66ae0 s12215-025-01256-y.pdf 9764072008c3399d1b31f7cb4a8735eb6732cf7342bdce5e1de83fe52c74b127 s12215-025-01256-y.pdf Title: Reversible nilpotent centers with cubic nonlinearities Subject: Rendiconti del Circolo Matematico di Palermo Series 2, https://doi.org/10.1007/s12215-025-01256-y Keywords: Nilpotent centers; Reversible centers; Cubic polynomials differential systems Author: Leandro Bacelar Creator: Springer Producer: Acrobat Distiller 10.1.8 (Windows); modified using iText® 5.3.5 ©2000-2012 1T3XT BVBA (SPRINGER SBM; licensed version) CreationDate: Fri Jun 13 15:17:59 2025 CEST ModDate: Fri Jun 13 17:45:48 2025 CEST Custom Metadata: yes Metadata Stream: yes Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 25 Encrypted: no Page size: 439.37 x 666.142 pts Page rot: 0 File size: 644999 bytes Optimized: no PDF version: 1.4 name type encoding emb sub uni object ID 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CEST RepresentationInformation: s12215-025-01256-y.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-07-10 13:21:34 CEST Size: 644999 Format: PDF Version: 1.4 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 1499 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseOutlines Language: EN Outlines: Item: Title: Reversible nilpotent centers with cubic nonlinearities Destination: Doc-Start Children: Item: Title: Abstract Destination: abscnt.2 Item: Title: 1 Introduction and statement of the main results Destination: section.1 Item: Title: 2 Analysis of system (3) Destination: section.2 Children: Item: Title: 2.1 First integrals Destination: subsection.2.1 Item: Title: 2.2 The finite singular points Destination: subsection.2.2 Item: Title: 2.3 The infinite singular points Destination: subsection.2.3 Item: Title: 2.4 Phase portraits in the Poincaré disc Destination: subsection.2.4 Item: Title: 3 Analysis of system (4) Destination: section.3 Children: Item: Title: 3.1 First integrals Destination: subsection.3.1 Item: Title: 3.2 The finite singular points Destination: subsection.3.2 Item: Title: 3.3 The infinite singular points Destination: subsection.3.3 Item: Title: 3.4 Phase portraits in the Poincaré disc Destination: subsection.3.4 Item: Title: 4 Analysis of system (5) Destination: section.4 Children: Item: Title: 4.1 First integrals Destination: subsection.4.1 Item: Title: 4.2 The finite singular points Destination: subsection.4.2 Item: Title: 4.3 The infinite singular points Destination: subsection.4.3 Item: Title: 4.4 Phase portraits in the Poincaré disc Destination: subsection.4.4 Item: Title: 5 Analysis of system (6) Destination: section.5 Children: Item: Title: 5.1 First integrals Destination: subsection.5.1 Item: Title: 5.2 The finite singular points Destination: subsection.5.2 Item: Title: 5.3 The infinite singular points Destination: subsection.5.3 Item: Title: 5.4 Phase portraits in the Poincaré disc Destination: subsection.5.4 Item: Title: 6 Analysis of system (7) Destination: section.6 Children: Item: Title: 6.1 First integrals Destination: subsection.6.1 Item: Title: 6.2 The finite singular points Destination: subsection.6.2 Item: Title: 6.3 The infinite singular points Destination: subsection.6.3 Item: Title: 6.4 Phase portraits in the Poincaré disc Destination: subsection.6.4 Item: Title: 7 Appendix Destination: section.7 Children: Item: Title: 7.1 Singular points Destination: subsection.7.1 Item: Title: 7.2 Vertical blow up Destination: subsection.7.2 Item: Title: 7.3 The Poincaré compactification Destination: subsection.7.3 Item: Title: Acknowledgements Destination: equation.7.31 Item: Title: References Destination: myseccnt.1 Info: Title: Reversible nilpotent centers with cubic nonlinearities Author: Leandro Bacelar Subject: Rendiconti del Circolo Matematico di Palermo Series 2, 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