Asymptotic Continuous Orbit Equivalence of Smale Spaces and Ruelle Algebras

Matsumoto, Kengo

Canadian journal of mathematics, Tome 71 (2019) no. 5, pp. 1243-1296

Résumé

In the first part of the paper, we introduce notions of asymptotic continuous orbit equivalence and asymptotic conjugacy in Smale spaces and characterize them in terms of their asymptotic Ruelle algebras with their dual actions. In the second part, we introduce a groupoid $C^{\ast }$-algebra that is an extended version of the asymptotic Ruelle algebra from a Smale space and study the extended Ruelle algebras from the view points of Cuntz–Krieger algebras. As a result, the asymptotic Ruelle algebra is realized as a fixed point algebra of the extended Ruelle algebra under certain circle action.

Détail

DOI : 10.4153/CJM-2018-012-x

Mots-clés : hyperbolic dynamics, Smale space, Ruelle algebra, groupoid, zeta function, continuous orbit equivalence, shifts of finite type, Cuntz-Krieger algebra

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