Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/8155
Title: Perturbations from an elliptic Hamiltonian of degree four
Authors: DUMORTIER, Freddy 
LI, Chengzhi
Issue Date: 2000
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Source: Bates, PW & Lu, K & Xu, D (Ed.) PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS AND COMPUTATIONAL SIMULATIONS. p. 66-70.
Abstract: The paper deals with a complete study of the number of zeros of Abelian integrals, related to perturbations of the Hamilonian vector fields with an elliptic Hamiltonian of degree four: (x) over dot = y, (y) over dot = P(x) + deltaQ(x)y, where P and Q are polynomials of degree respectively 3 and 2, and delta small. We prove that if the unperturbed Hamiltonian vector field has a saddle loop, a cuspidal loop or a global center, then for the perturbed system the corresponding maximum number of zeros of Abelian integral is respectively 2, 4 and 4. In the last case, the perturbed system may have a quadruple limit cycle, as was conjectured in (11).
Notes: Limburgs Univ Ctr, Diepenbeek, B-3590 Belgium.Dumortier, F, Limburgs Univ Ctr, Univ Campus, Diepenbeek, B-3590 Belgium.
Document URI: http://hdl.handle.net/1942/8155
ISBN: 981-02-4268-9
ISI #: 000168276000012
Category: C1
Type: Proceedings Paper
Validations: ecoom 2002
Appears in Collections:Research publications

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