On the number of limit cycles bifurcating from a non-global degenerated center

Armengol Gasull; Chengzhi Li; Changjian Liu

doi:https://doi.org/10.1016/j.jmaa.2006.06.047

On the number of limit cycles bifurcating from a non-global degenerated center

Armengol Gasull, Chengzhi Li, Changjian Liu

Department of Mathematics

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

8 Citations (Scopus)

Abstract

We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system (1 + x) d H = 0, where H is the quasi-homogeneous Hamiltonian H (x, y) = x2 k / (2 k) + y2 / 2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. © 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	268-280
Journal	Journal of Mathematical Analysis and Applications
Volume	329
DOIs	https://doi.org/10.1016/j.jmaa.2006.06.047
Publication status	Published - 1 May 2007

Keywords

Abelian integral
Degenerated center
Limit cycle
Planar vector field

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title = "On the number of limit cycles bifurcating from a non-global degenerated center",

abstract = "We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system (1 + x) d H = 0, where H is the quasi-homogeneous Hamiltonian H (x, y) = x2 k / (2 k) + y2 / 2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. {\textcopyright} 2006 Elsevier Inc. All rights reserved.",

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author = "Armengol Gasull and Chengzhi Li and Changjian Liu",

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T1 - On the number of limit cycles bifurcating from a non-global degenerated center

AU - Gasull, Armengol

AU - Li, Chengzhi

AU - Liu, Changjian

PY - 2007/5/1

Y1 - 2007/5/1

N2 - We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system (1 + x) d H = 0, where H is the quasi-homogeneous Hamiltonian H (x, y) = x2 k / (2 k) + y2 / 2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. © 2006 Elsevier Inc. All rights reserved.

AB - We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system (1 + x) d H = 0, where H is the quasi-homogeneous Hamiltonian H (x, y) = x2 k / (2 k) + y2 / 2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. © 2006 Elsevier Inc. All rights reserved.

KW - Abelian integral

KW - Degenerated center

KW - Limit cycle

KW - Planar vector field

U2 - https://doi.org/10.1016/j.jmaa.2006.06.047

DO - https://doi.org/10.1016/j.jmaa.2006.06.047

M3 - Article

VL - 329

SP - 268

EP - 280

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -