Alien limit cycles in Liénard equations
Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Dumortier, Freddy (Universiteit Hasselt(Belgium). Dept. Wiskunde)
Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)

Date:	2013
Abstract:	This paper aims at providing an example of a family of polynomial Liénard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. The Hamiltonian represents a truncated pendulum of degree 4. In comparison to a former polynomial example, not only the equations are simpler but a lot of tedious calculations can be avoided, making the example also interesting with respect to simplicity in treatment.
Grants:	Ministerio de Ciencia e Innovación MTM2011-22751
Note:	Agraïments: The second author thanks the Universitat de les Illes Balears (UIB) for its support as invited professor during the period November to December, 2011.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Abelian integrals ; Hamiltonian perturbation ; Liénard equation ; Limit cycles ; Planar vector field ; Two-saddle cycle ; Limit cycle ; Abelian integral
Published in:	Journal of differential equations, Vol. 254 (2013) , p. 1582-1600, ISSN 1090-2732

DOI: 10.1016/j.jde.2012.11.005

Postprint 20 p, 399.5 KB

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