The cyclicity of the period annulus of a
  quadratic reversible system with a hemicycle

Peng, Linping; Lei, Yazhi

doi:10.3934/dcds.2011.30.873

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Introduction and Statement Of The Main Results1

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“…Some concrete applications of that theory to planar differential systems of low degree can be seen in [6,16]. In higher dimension, the averaging theory can be also used, for example, for the study of the Hopf bifurcation, see [12,13].…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Limit Cycles Coming from Some Uniform Isochronous Centers

Liang

Llibre

Torregrosa

2016

Advanced Nonlinear Studies

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Abstract. This article is about the weak 16-th Hilbert problem, i.e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. More precisely, we consider the uniform isochronous centerṡof degree 2n+3 and we perturb them inside the class of all polynomial differential systems of degree 2n + 3. For n = 0, 1 we provide the maximum number of limit cycles, 3 and 8 respectively, that can bifurcate from the periodic orbits of these centers using averaging theory of first order, or equivalently Abelian integrals. For n = 2 we show that at least 12 limit cycles can bifurcate from the periodic orbits of the center.

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%