Classification of Global Phase Portrait of Planar Quintic Quasi-Homogeneous Coprime Polynomial Systems

This paper is devoted to the complete classification of global phase portraits (short for GPP) of quasi-homogeneous but non-homogeneous coprime planar quintic polynomial differential systems (short for QCQS). We firstly study the canonical forms of QCQS. It is shown that these canonical forms can ha...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 16; no. 2; pp. 417 - 451
Main Authors Qiu, BaoHua, Liang, HaiHua
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2017
Springer Nature B.V
Subjects
Canonical forms
Classification
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Singularity (mathematics)
Topology
Quasi-homogeneous
34C05
37G05
Global phase portraits
Canonical forms
34C20
Quintic
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Summary:This paper is devoted to the complete classification of global phase portraits (short for GPP) of quasi-homogeneous but non-homogeneous coprime planar quintic polynomial differential systems (short for QCQS). We firstly study the canonical forms of QCQS. It is shown that these canonical forms can have 0, 1, 2, 4 parameters. Then, we investigate the global topological structures of all canonical forms, by using the quasi-homogeneous blow-up technique for the finite singularities and the Poincaré–Lyapunov compactification for the infinite singularities. We finally perform a topological classification for the set of GPP.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-016-0199-7