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Title: Perturbations from an elliptic Hamiltonian of degree four - II. Cuspidal loop
Authors: DUMORTIER, Freddy
LI, Chengzhi
Issue Date: 2001
Citation: 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
URI: http://hdl.handle.net/1942/5012
DOI: 10.1006/jdeq.2000.3978
ISI #: 000171278800002
ISSN: 0022-0396
Category: A1
Type: Journal Contribution
Validation: ecoom, 2002
Appears in Collections: Research publications

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