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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/5314

Title: Perturbations from an elliptic Hamiltonian of degree four I. Saddle loop and two saddle cycle
Authors: DUMORTIER, Freddy
LI, Chengzhi
Issue Date: 2001
Citation: Journal of differential equations, 176(1). p. 114-157
Abstract: The paper deals with Lienard equations of the form (x) over dot = y, (y) over dot = P(x) + yQ(x) with P and Q polynomials of degree respectively 3 and 2. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree 4 and especially to the study of the related elliptic integrals. Besides some general results the paper contains a complete treatment of the Saddle Loop case and the Two Saddle Cycle case. It is proven that the related elliptic integrals have at most two zeros, respectively one zero. the multiplicity taken into account. The bifurcation diagram of the zeros is also obtained.
URI: http://hdl.handle.net/1942/5314
DOI: 10.1006/jdeq.2000.3977
ISI #: 000171903600004
ISSN: 0022-0396
Category: A1
Type: Journal Contribution
Validation: ecoom, 2002
Appears in Collections: Research publications

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