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http://hdl.handle.net/1942/5012
Title: | Perturbations from an elliptic Hamiltonian of degree four - II. Cuspidal loop | Authors: | DUMORTIER, Freddy LI, Chengzhi |
Issue Date: | 2001 | Publisher: | ACADEMIC PRESS INC | Source: | Journal of differential equations, 175(2). p. 209-243 | Abstract: | The paper deals with Lienard equations of the form x = y, y = P(x) + yQ(x) with P and Q polynomials of degree respectively 3 and 2. Attention goes to perturbations of the Hamiltonian vector field with an elliptic Hamiltonian of degree 4, exhibiting a cuspidal loop. It is proven that the least upper bound for the number of zeros of the related elliptic integral is four, and this upper bound is a sharp one. This permits to prove the existence of Lienard equations of type (3, 2) with at least four limit cycles. The paper also contains a complete result on the respective number of "small" and "large" limit cycles | Keywords: | CRITICAL-POINTS; NUMBER; PERIOD | Document URI: | http://hdl.handle.net/1942/5012 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1006/jdeq.2000.3978 | ISI #: | 000171278800002 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2002 |
Appears in Collections: | Research publications |
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