Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/1565
Title: Abelian integrals and limit cycles
Authors: DUMORTIER, Freddy 
Roussarie, R.
Issue Date: 2006
Publisher: Elsevier
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 227(1). p. 116-165
Abstract: The paper deals with generic perturbations from a Hamiltonian planar vector field and more precisely with the number and bifurcation pattern of the limit cycles. In this paper we show that near a 2-saddle cycle, the number of limit cycles produced in unfoldings with one unbroken connection, can exceed the number of zeros of the related Abelian integral, even if the latter represents a stable elementary catastrophe. We however also show that in general, finite codimension of the Abelian integral leads to a finite upper bound on the local cyclicity. In the treatment, we introduce the notion of simple asymptotic scale deformation.
Keywords: Planar vector field; Hamiltonian perturbation; Limit cycle; Abelian integral; Two-saddle cycle; Asymptotic scale deformation
Document URI: http://hdl.handle.net/1942/1565
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2005.08.015
ISI #: 000238729700006
Category: A1
Type: Journal Contribution
Validations: ecoom 2007
Appears in Collections:Research publications

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