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

By S. Crovisier, E. Pujals. 2010

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We prove that any diffeomorphism of a compact manifold can be approximated in the $$C^1$$C1 topology by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f5bf4af0b6a79e2ba2c72a39f9e97473fa67bfcb