Orders of accumulation of entropy

• Autorzy: David Burguet , Kevin McGoff
• Języki publikacji: EN

Abstrakty

EN

For a continuous map T of a compact metrizable space X with finite topological entropy, the order of accumulation of entropy of T is a countable ordinal that arises in the context of entropy structures and symbolic extensions. We show that every countable ordinal is realized as the order of accumulation of some dynamical system. Our proof relies on functional analysis of metrizable Choquet simplices and a realization theorem of Downarowicz and Serafin. Further, if M is a metrizable Choquet simplex, we bound the ordinals that appear as the order of accumulation of entropy of a dynamical system whose simplex of invariant measures is affinely homeomorphic to M. These bounds are given in terms of the Cantor-Bendixson rank of $\overline{ex(M)}$, the closure of the extreme points of M, and the relative Cantor-Bendixson rank of $\overline{ex(M)}$ with respect to ex(M). We also address the optimality of these bounds.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 216
• Numer: 1
• Strony: 1-53

Daty

wydano

2012

Twórcy

autor

David Burguet

• CMLA-ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France

autor

Kevin McGoff

• Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, U.S.A.

Identyfikatory

DOI

10.4064/fm216-1-1