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arXiv · 1403.3572

A dichotomy in area-preserving reversible maps

Mario Bessa·Alexandre Rodrigues
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Abstract

In this paper we study R-reversible area-preserving maps f on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that Ro f=f^{-1}o R where R is an isometric involution on M. We obtain a C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits. As a consequence we obtain the proof of the stability conjecture for this class of maps. Along the paper we also derive the C1-closing lemma for reversible maps and other perturbation toolboxes.

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Mario Bessa, Alexandre Rodrigues. 2014-03-14. A dichotomy in area-preserving reversible maps. https://arxiv.org/abs/1403.3572

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