Hopf bifurcation at infinity for planar vector fields

Begoña Alarcón; Víctor Guíñez; Carlos Gutierrez

doi:10.3934/dcds.2007.17.247

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2007, Volume 17, Issue 2: 247-258. Doi: 10.3934/dcds.2007.17.247

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Hopf bifurcation at infinity for planar vector fields

1.
Universitat de València, Departament de Geometria y Topologia, Dr. Moliner s/n CP: 46100 Burjassot, València
2.
Universidad de Santiago de Chile, Departamento de Matemática y C.C., Casilla 307, Correo 2, Santiago
3.
ICMC-USP, São Carlos, Caixa Postal 668, CEP 13560-970, São Carlos, SP

Received: December 2005

Revised: September 2006

Published: May 2007

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Abstract

We study, from a new point of view, families of planar vector fields without singularities $ \{ X_{\mu}$ : $-\varepsilon < \mu < \varepsilon\} $ defined on the complement of an open ball centered at the origin such that, at $\mu=0$, infinity changes from repellor to attractor, or vice versa. We also study a sort of local stability of some $C^1$ planar vector fields around infinity.

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Mathematics Subject Classification: 37G10, 37G15, 34K18.

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