The geometry of the real planar polynomial differential systems having their orbits embedded in conics

Jaume Llibre; Adam Mahdi; Joaquim Roé

doi:https://doi.org/10.1080/14689367.2011.588593

The geometry of the real planar polynomial differential systems having their orbits embedded in conics

Jaume Llibre, Adam Mahdi, Joaquim Roé

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

We classify and provide the global phase portraits in the Poincare disc of all real planar polynomial differential systems having their orbits embedded in conics. This is achieved via the real affine classification of the pencils of conics, and each type corresponds to an equisingularity type of pencil. All such polynomial vector fields have degree less than or equal to 3. Also, when the degree is 3, infinity is filled with singular points. © 2011 Taylor & Francis.

Original language	English
Pages (from-to)	287-321
Journal	Dynamical Systems
Volume	26
DOIs	https://doi.org/10.1080/14689367.2011.588593
Publication status	Published - 1 Sep 2011

Keywords

pencil of conics
phase portraits
polynomial vector field
rational function

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AB - We classify and provide the global phase portraits in the Poincare disc of all real planar polynomial differential systems having their orbits embedded in conics. This is achieved via the real affine classification of the pencils of conics, and each type corresponds to an equisingularity type of pencil. All such polynomial vector fields have degree less than or equal to 3. Also, when the degree is 3, infinity is filled with singular points. © 2011 Taylor & Francis.

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KW - phase portraits

KW - polynomial vector field

KW - rational function

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The geometry of the real planar polynomial differential systems having their orbits embedded in conics

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Keywords

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