Strange attractors in higher dimensions

  • Marcelo Viana
Article

DOI: 10.1007/BF01231695

Cite this article as:
Viana, M. Bol. Soc. Bras. Mat (1993) 24: 13. doi:10.1007/BF01231695

Abstract

We consider generic one-parameter families of diffeomorphisms on a manifold of arbitrary dimension, unfolding a homoclinic tangency associated to a sectionally dissipative saddle point (the product of any pair of eigenvalues has norm less than 1). We prove that such families exhibit strange attractors in a persistent way: for a positive Lebesgue measure set of parameter values. In the two-dimensional case this had been obtained in a joint work with L. Mora, based on and extending the results of Benedicks-Carleson on the quadratic family in the plane.

Copyright information

© Sociedade Brasileira de Matemática 1993

Authors and Affiliations

  • Marcelo Viana
    • 1
    • 2
  1. 1.Departamento de MatemáticaUniversidade do PortoPortoPortugal
  2. 2.Instituto de Matemática Pura e Aplicada, IMPARio de JaneiroBrasil

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