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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exact number of limit cycles for a family of rigid systems


Authors: A. Gasull and J. Torregrosa
Journal: Proc. Amer. Math. Soc. 133 (2005), 751-758
MSC (2000): Primary 34C07, 37G15; Secondary 34C25, 37C27
Published electronically: October 7, 2004
MathSciNet review: 2113924
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Abstract: For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condition that allows us to separate the existence and the nonexistence of limit cycles can be described, it is very intricate.


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Additional Information

A. Gasull
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C 08193, Bellaterra, Barcelona, Spain
Email: gasull@mat.uab.es

J. Torregrosa
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C 08193, Bellaterra, Barcelona, Spain
Email: torre@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07542-2
PII: S 0002-9939(04)07542-2
Keywords: Bifurcation, limit cycle, rotated vector field, rigid system
Received by editor(s): September 5, 2003
Received by editor(s) in revised form: October 6, 2003
Published electronically: October 7, 2004
Additional Notes: This work was supported by DGES No.\ BFM2002-04236-C02-2 and CONACIT 2001SGR-00173.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society