Genericity of infinite entropy for maps with low regularity

Autor(es)

De Faria, Edson ^[1] ; Hazard, Peter ^[2] ; Tresser, Charles ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil

^[2] Univ Fed Fluminense, Inst Matemat & Estat, Niteroi, RJ - Brazil

^[3] 301 W 118th St 8B, New York, NY 10026 - USA

• Tipo de documento: Artigo Científico
• Fonte: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE; v. 22, n. 2, p. 601-664, 2021.
• Citações Web of Science: 0

Resumo

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 Holder or the Sobolev topologies, topological entropy is generically infinite. We also prove versions of the C-1-Closing Lemma in either of these spaces. Finally, we give examples of homeomorphisms with infinite topological entropy which are Holder and/or Sobolev of every exponent. (AU)

• Processo FAPESP: 15/17909-7 - Regularidade e fronteira do caos
• Beneficiário: Edson de Faria
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional