On the limit cycles of linear differential systems with homogeneous nonlinearities

Jaume Llibre; Xiang Zhang

doi:https://doi.org/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

Access to Document

https://doi.org/10.4153/CMB-2015-062-1

https://ddd.uab.cat/record/145301

Cite this

@article{0c5284c9a773467db26654340feab3d6,

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

abstract = "{\textcopyright} Canadian Mathematical Society 2015. We consider the class of polynomial di{\`o}erential 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 di{\`o}erential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.",

keywords = "Di{\`o}erential equations on the cylinder, Limit cycles, Polynomial di{\`o}erential system",

author = "Jaume Llibre and Xiang Zhang",

year = "2015",

month = dec,

day = "1",

doi = "https://doi.org/10.4153/CMB-2015-062-1",

language = "English",

volume = "58",

pages = "818--823",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

publisher = "Canadian Mathematical Society",

number = "4",

}

TY - JOUR

T1 - On the limit cycles of linear differential systems with homogeneous nonlinearities

AU - Llibre, Jaume

AU - Zhang, Xiang

PY - 2015/12/1

Y1 - 2015/12/1

N2 - © 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.

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

U2 - https://doi.org/10.4153/CMB-2015-062-1

DO - https://doi.org/10.4153/CMB-2015-062-1

M3 - Article

VL - 58

SP - 818

EP - 823

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 4

ER -

On the limit cycles of linear differential systems with homogeneous nonlinearities

Abstract

Keywords

Access to Document

Fingerprint

Cite this