Invariant algebraic curves for the cubic Liénard system with linear damping

J. Chavarriga; I. A. García; J. Llibre; H. Zoładek

doi:10.1016/j.bulsci.2006.03.013

Invariant algebraic curves for the cubic Liénard system with linear damping

J. Chavarriga, I. A. García, J. Llibre, H. Zoładek

Department of Mathematics

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

10 Citations (Scopus)

Abstract

We show that the system over(x, ̇) = y, over(y, ̇) = - f (x) y - g (x) with f, g polynomials of degree 1 and 3 respectively cannot have simultaneously an algebraic invariant curve and a limit cycle. © 2006.

Original language	English
Pages (from-to)	428-441
Journal	Bulletin des Sciences Mathematiques
Volume	130
Issue number	5
DOIs	https://doi.org/10.1016/j.bulsci.2006.03.013
Publication status	Published - 1 Jul 2006

Keywords

Algebraic limit cycles
Liénard system
Limit cycles

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title = "Invariant algebraic curves for the cubic Li{\'e}nard system with linear damping",

abstract = "We show that the system over(x,{\. }) = y, over(y,{\. }) = - f (x) y - g (x) with f, g polynomials of degree 1 and 3 respectively cannot have simultaneously an algebraic invariant curve and a limit cycle. {\textcopyright} 2006.",

keywords = "Algebraic limit cycles, Li{\'e}nard system, Limit cycles",

author = "J. Chavarriga and Garc{\'i}a, {I. A.} and J. Llibre and H. Zo{\l}adek",

year = "2006",

month = jul,

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doi = "10.1016/j.bulsci.2006.03.013",

language = "English",

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journal = "Bulletin des Sciences Mathematiques",

issn = "0007-4497",

publisher = "Elsevier Masson SAS",

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TY - JOUR

T1 - Invariant algebraic curves for the cubic Liénard system with linear damping

AU - Chavarriga, J.

AU - García, I. A.

AU - Llibre, J.

AU - Zoładek, H.

PY - 2006/7/1

Y1 - 2006/7/1

N2 - We show that the system over(x, ̇) = y, over(y, ̇) = - f (x) y - g (x) with f, g polynomials of degree 1 and 3 respectively cannot have simultaneously an algebraic invariant curve and a limit cycle. © 2006.

AB - We show that the system over(x, ̇) = y, over(y, ̇) = - f (x) y - g (x) with f, g polynomials of degree 1 and 3 respectively cannot have simultaneously an algebraic invariant curve and a limit cycle. © 2006.

KW - Algebraic limit cycles

KW - Liénard system

KW - Limit cycles

U2 - 10.1016/j.bulsci.2006.03.013

DO - 10.1016/j.bulsci.2006.03.013

M3 - Article

VL - 130

SP - 428

EP - 441

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

SN - 0007-4497

IS - 5

ER -