Stable weak shadowable symplectomorphisms are partially hyperbolic
Commun. Korean Math. Soc. 2014 Vol. 29, No. 2, 285-293
https://doi.org/10.4134/CKMS.2014.29.2.285
Printed April 1, 2014
M\'{a}rio Bessa and Sandra Vaz
Universidade Da Beira Interior, Universidade Da Beira Interior
Abstract : Let $M$ be a closed, symplectic connected Riemannian manifold and $f$ a symplectomorphism on $M$. We prove that if $f$ is $C^1$-stably weak shadowable on $M$, then the whole manifold $M$ admits a partially hyperbolic splitting.
Keywords : partial hyperbolicity, weak shadowing, symplectomorphisms
MSC numbers : Primary 37D30, 37C50; Secondary 37J10
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