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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Genericity of infinite entropy for maps with low regularity

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Author(s):
De Faria, Edson [1] ; Hazard, Peter [2] ; Tresser, Charles [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE; v. 22, n. 2, p. 601-664, 2021.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 15/17909-7 - Regularity and the boundary of chaos
Grantee:Edson de Faria
Support Opportunities: Research Grants - Visiting Researcher Grant - International