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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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