Web of Science: 24 citations, Scopus: 25 citations, Google Scholar: citations
Limit cycles appearing from the perturbation of a system with a multiple line of critical points
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2012
Abstract: Consider the planar ordinary differential equation ˙x = −y(1 − y)m, y˙ = x(1 − y)m, where m is a positive integer number. We study the maximum number of zeroes of the Abelian integral M that controls the limit cycles that bifurcate from the period annulus of the origin when we perturb it with an arbitrary polynomial vector field. One of the key points of our approach is that we obtain a simple expression of M based on some successive reductions of the integrals appearing during the procedure.
Grants: Ministerio de Ciencia e Innovación MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note: Agraïments: The second author is partially supported by NSFC-10831003 and by AGAUR grant number 2009PIV00064.
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Subject: Limit cycles ; Weak Hilbert's 16th Problem ; Abelian integrals ; Bifurcation of periodic orbits
Published in: Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 278-285, ISSN 0362-546X

DOI: 10.1016/j.na.2011.08.032


Postprint
11 p, 279.4 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-05-06, last modified 2022-05-24



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