Stable weakly shadowable volume-preserving systems are volume-hyperbolic

Bessa, Mário; Lee, Manseob; Vaz, Sandra

http://hdl.handle.net/10400.6/12421

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Authors

Bessa, Mário

Lee, Manseob

Vaz, Sandra

Abstract(s)

We prove that any C1-stable 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

Weak shadowin Dominated splitting Hyperbolicity

URI

http://hdl.handle.net/10400.6/12421

Citation

Bessa, M., Lee, M. & Vaz, S. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta. Math. Sin.-English Ser. 30, 1007–1020 (2014). https://doi.org/10.1007/s10114-014-3093-8