A dichotomy in area-preserving reversible maps

Bessa, Mário; Rodrigues, Alexandre A. P.

http://hdl.handle.net/10400.2/13895

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Authors

Bessa, Mário

Rodrigues, Alexandre A. P.

Abstract(s)

In this paper we study R-reversible area-preserving maps f : M → M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that R ◦ f = f−1 ◦ R where R: M → M is an isometric involution. We obtain a C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the C1-Closing Lemma for reversible maps and other perturbation toolboxes.