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Asymptotic Continuous Orbit Equivalence of Smale Spaces and Ruelle Algebras
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 71 / Issue 5 / October 2019
- Published online by Cambridge University Press:
- 09 January 2019, pp. 1243-1296
- Print publication:
- October 2019
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- Article
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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.
