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April  2007, 17(2): 247-258. doi: 10.3934/dcds.2007.17.247

Hopf bifurcation at infinity for planar vector fields

Begoña Alarcón 1, , Víctor Guíñez 2, and  Carlos Gutierrez 3,

1. 

Universitat de València, Departament de Geometria y Topologia, Dr. Moliner s/n CP: 46100 Burjassot, València, Spain
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  November 2006

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.
Keywords: Hopf bifurcation, vector field, Poincaré index., singular points.
Mathematics Subject Classification: 37G10, 37G15, 34K1.
Citation: Begoña Alarcón, Víctor Guíñez, Carlos Gutierrez. Hopf bifurcation at infinity for planar vector fields. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 247-258. doi: 10.3934/dcds.2007.17.247
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