Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms

Details Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms

2010-11-16

arxiv.org/abs/1011.3836v1

Mathematics

Dynamical Systems

Scientific paper

We prove that any diffeomorphism of a compact manifold can be approximated in
topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a
homoclinic tangency or a heterodimensional cycle) or by one which is
essentially hyperbolic (it has a finite number of transitive hyperbolic
attractors with open and dense basin of attraction).

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