Papers published in the English version of the journal

Hyperbolicity for Conservative Diffeomorphisms

A. Zamani Bahabadi

Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract: This paper introduces the notion of robust hyperbolicity along periodic orbits homoclinically related to $p$ (RNUHP) for conservative diffeomorphisms. It is proved that if $f \in Diff_m ^{1+} (M)$ is RNUHP, then $f$ is Anosov. It is also shown that $f$ admits a dominated splitting, provided that $f$ is expansive conservative stable.

Keywords: hyperbolicity, homoclinic class, dominated splitting.

Received: 28.01.2017
Revised: 10.07.2017

Language: English

 English version: Mathematical Notes, 2018, 103:3, 490–494

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