# American Institute of Mathematical Sciences

May  2008, 20(2): 335-405. doi: 10.3934/dcds.2008.20.335

## Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets

 1 IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil

Received  June 2006 Revised  July 2007 Published  November 2007

Given a topologically hyperbolic attracting set of a smooth three dimensional Kupka-Smale diffeomorphism, it is proved under some dissipation hypothesis, that either the set is hyperbolic or the diffeomorphism is $C^1-$approximated by another one exhibiting either a heterodimensional cycle or a homoclinic tangency.
Citation: Enrique R. Pujals. Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets. Discrete & Continuous Dynamical Systems - A, 2008, 20 (2) : 335-405. doi: 10.3934/dcds.2008.20.335
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