A Dichotomy in Area-Preserving Reversible Maps

作者：Bessa Mario; Rodrigues Alexandre A P^*

来源：Qualitative Theory of Dynamical Systems, 2016, 15(2): 309-326.

DOI：10.1007/s12346-015-0155-y

• Reversing symmetry
• Area-preserving map
• Closing Lemma
• Elliptic point

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 circle f = f(-1) circle R where R : M -> M is an isometric involution. We obtain a C-1-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 C-1-Closing Lemma for reversible maps and other perturbation toolboxes.

• 出版日期2016-10