English

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.

Keywords

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

R2 v1 2026-06-21T21:40:21.152Z