Density of hyperbolicity and homoclinic bifurcation for 3D-diffeomorphism in attracting regions.

Enrique R. Pujals

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In the present paper it is proved that given a maximal invariant attracting homoclinic class for a smooth three dimensional Kupka-Smale diffeomorphism, it follows that the homoclinic class is either hyperbolic or the diffeomorphisms is $C^1-$ approximated by another map exhibiting a homoclinic tangency or a heterodimensional cycle.

Anexos:

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