Partial hyperbolicity far from homoclinic bifurcations
Dynamical Systems
2008-09-30 v1
Abstract
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially hyperbolic (its chain-recurrent set splits into partially hyperbolic pieces whose centre bundles have dimensions less or equal to two). We also study in a more systematic way the central models introduced in arXiv:math/0605387.
Cite
@article{arxiv.0809.4965,
title = {Partial hyperbolicity far from homoclinic bifurcations},
author = {Sylvain Crovisier},
journal= {arXiv preprint arXiv:0809.4965},
year = {2008}
}