A Dichotomy in Area-Preserving Reversible Maps

• Mário Bessa ^[1] ; Alexandre A. P. Rodrigues ^[2]
  1. [1] Universidade da Beira Interior

     Universidade da Beira Interior

     Covilhã (Conceição), Portugal

     
  2. [2] Universidade Do Porto

     Universidade Do Porto

     Santo Ildefonso, Portugal

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 2, 2016, págs. 309-326
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.