On the limit cycles of linear differential systems with homogeneous nonlinearities

Jaume Llibre; Xiang Zhang

doi:10.4153/CMB-2015-062-1

On the limit cycles of linear differential systems with homogeneous nonlinearities

Jaume Llibre, Xiang Zhang

Department of Mathematics

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

2 Citations (Scopus)

Abstract

© Canadian Mathematical Society 2015. We consider the class of polynomial diòerential systems of the form x = λx-y+Pn(x, y), Y = x +jy+Qn(x, y), where Pn and n are homogeneous polynomials of degree n. For this class of diòerential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.

Original language	English
Pages (from-to)	818-823
Journal	Canadian Mathematical Bulletin
Volume	58
Issue number	4
DOIs	https://doi.org/10.4153/CMB-2015-062-1
Publication status	Published - 1 Dec 2015

Keywords

Diòerential equations on the cylinder
Limit cycles
Polynomial diòerential system

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title = "On the limit cycles of linear differential systems with homogeneous nonlinearities",

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AB - © Canadian Mathematical Society 2015. We consider the class of polynomial diòerential systems of the form x = λx-y+Pn(x, y), Y = x +jy+Qn(x, y), where Pn and n are homogeneous polynomials of degree n. For this class of diòerential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.

KW - Diòerential equations on the cylinder

KW - Limit cycles

KW - Polynomial diòerential system

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