Stable weakly shadowable volume-preserving systems are volume-hyperbolic
Dynamical Systems
2012-07-25 v1
Abstract
We prove that any C1-stably weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E + F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.
Cite
@article{arxiv.1207.5546,
title = {Stable weakly shadowable volume-preserving systems are volume-hyperbolic},
author = {Mario Bessa and Manseob Lee and Sandra Vaz},
journal= {arXiv preprint arXiv:1207.5546},
year = {2012}
}
Comments
17 pages