Prevalence of hyperbolicity for complex singular cycles |
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| Authors: | R Labarca B San Martin |
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| Institution: | (1) Departmento de Matemática y C.C., Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile;(2) Departamento de Matemática, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile |
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| Abstract: | In this article we consider two kinds of complex singular cycles arising for vector fields defined on three-dimensional manifolds. We prove that, under some generic conditions, any one parameter family of vector fields passing through these cycles has the following property: Hyperbolicity is a prevalent phenomena.Dedicated to the memory of Professor R. Mañé.Partially Supported by Fondecyt 1941080 and Dirección de Investigación Universidad de Santiago de Chile |
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