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arXiv · 1207.5546

Stable weakly shadowable volume-preserving systems are volume-hyperbolic

Mario Bessa·Manseob Lee·Sandra Vaz
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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.

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Mario Bessa, Manseob Lee, Sandra Vaz. 2012-07-23. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. https://arxiv.org/abs/1207.5546

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