Minimal homeomorphisms and approximate conjugacy in measure
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Publication:938804
zbMath1167.37011arXivmath/0501262MaRDI QIDQ938804
Publication date: 27 August 2008
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
Abstract: Let X be an infinite compact metric space with finite covering dimension. Let $afhpa,�t: X o X$ be two minimal homeomorphisms. Suppose that the range of $K_0$-groups of both crossed product C*-algebras s are dense in the space of real affine continuous functions. We show that $af$ and $�t$ are approximately conjugate uniformly in measure if and only if they have affine homeomorphic invariant probability measure spaces.
Full work available at URL: https://arxiv.org/abs/math/0501262
Classifications of (C^*)-algebras (46L35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dynamical systems and the theory of (C^*)-algebras (37A55)
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