Genericity of infinite entropy for maps with low regularity

• Edson De Faria ^[1] ; Peter Hazard ^[2] ; Charles Tresser
  1. [1] Instituto de Matemáticae Estatística USP, Brazil
  2. [2] Instituto de Matemáticae Estatística, UFF
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 2, 2021, págs. 601-664
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomor- phisms, with respect to either the H ̈older or the Sobolev topologies, topological entropy is generically infinite. We also prove versions of the C1-Closing Lemma in either of these spaces. Finally, we give examples of homeomorphisms with infinite topological entropy which are H ̈older and/or Sobolev of every exponent.