Asymptotic Continuous Orbit Equivalence of Smale Spaces and Ruelle Algebras
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AbstractIn 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.
1989 ◽
Vol 112
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pp. 71-112
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1999 ◽
Vol 125
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pp. 43-52
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2013 ◽
Vol 34
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pp. 2066-2092
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2018 ◽
Vol 29
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pp. 1850016
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2011 ◽
Vol 22
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pp. 1603-1610
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1997 ◽
Vol 09
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pp. 785-819
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2013 ◽
Vol 62
(6)
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pp. 1691-1716
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