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

DOI:
https://doi.org/10.1090/S0002-9939-04-07542-2

Published electronically:
October 7, 2004

MathSciNet review:
2113924

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-04-07542-2

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