Article Contents
Article Contents

Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets

• 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.
Mathematics Subject Classification: Primary: 37C05 , 37D05, 37G25, 37D30 ; Secondary: 37C70, 37C75.

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