COLÓQUIO MAP
“Topological Entropy and Regularity”
Prof. Peter Hazard (IME/USP)
Dia: 25 de novembro, sexta-feira, Auditório Antonio Gilioli, Sala 247/262, Bloco A, IMEUSP, das 16 às 17h, Café às 15h30, na sala 265. A (Chefia do MAP)
Transmissão online: http://www.ime.usp.br/comunicacao/eventos/cat.listevents/
Abstract:
Introduced by Adler, Konheim and McAndrew in the 1960's, topological entropy is a invariant under topological conjugacy which one can assign to an arbitrary continuous self-map or flow of a compact space. One of the reasons for studying this invariant is that, in several cases, positivity implies the system possesses some form of chaotic behaviour. However, it is very sensitive to changes in the regularity of the system. For example, one classical result, due to Yano, states that generic homeomorphisms of compact manifolds of dimension two or more have infinite topological entropy. Another example, due to Ito and independently Bowen, states that for C^1-diffeomorphisms of compact manifolds, the topological entropy is always bounded. After introducing the basic theory, I will describe recent work with E. de Faria and C. Tresser which investigates what occurs in intermediate regularities between these two results.
