On the density of hyperbolicity and homoclinic bifurcations for 3D-diffeomorphisms in attracting regions
Enrique R. Pujals - IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil (email)
In the present paper it is proved that given a
maximal invariant attracting homoclinic class
for a smooth three dimensional Kupka-Smale diffeomorphism, either the
diffeomorphisms is $C^1$ approximated by another one exhibiting a
homoclinic tangency or a heterodimensional cycle, or it
follows that the homoclinic class is conjugate to a hyperbolic set (in this case we say that the homoclinic class is "topologically hyperbolic").
Keywords: Dominated splittings, uniformly hyperbolic systems, bifurcations connected with nontransversal intersection.
Received: August 2005; Revised: March 2006; Published: June 2006.
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