2017/09/07 by de Faria, Edson, Hazard, Peter, Tresser, Charles
#26A16 (Secondary) #37B40 (Primary) #37E99 #46E35 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1709.02431
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 homeomorphisms, with respect to either the Hölder 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 Hölder and/or Sobolev of every exponent.