BIFURCATION OF LIMIT CYCLES IN SMALL PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE 5 WITH A CUSP

Ali Atabaigi; Hamid R. Z. Zangeneh

doi:10.11948/2011021

2011 Volume 1 Issue 3

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Ali Atabaigi, Hamid R. Z. Zangeneh. BIFURCATION OF LIMIT CYCLES IN SMALL PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE 5 WITH A CUSP[J]. Journal of Applied Analysis & Computation, 2011, 1(3): 299-313. doi: 10.11948/2011021

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Ali Atabaigi, Hamid R. Z. Zangeneh. BIFURCATION OF LIMIT CYCLES IN SMALL PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE 5 WITH A CUSP[J]. Journal of Applied Analysis & Computation, 2011, 1(3): 299-313. doi: 10.11948/2011021

BIFURCATION OF LIMIT CYCLES IN SMALL PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE 5 WITH A CUSP

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111

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Abstract

Abstract

This paper deals with small perturbations of a class of hyperelliptic Hamiltonian system, which is a Liénard system of the form ẋ=y, ẏ=Q₁(x) + εyQ₂(x) with Q₁ and Q₂ polynomials of degree 4 and 3, respectively. It is shown that this system can undergo degenerated Hopf bifurcation and Poincaré bifurcation, which emerge at most three limit cycles for ε sufficiently small.
- Hyper-elliptic Hamiltonian system /
- Abelian integrals /
- Hilbert's 16th problem /
- Limit cycles
MSC: 34C07;34C08;37G15;34M50

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