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The Rokhlin lemma for homeomorphisms of a Cantor set | | Sergey Bezuglyi
; Anthony H. Dooley
; Konstantin Medynets
; | | Date: |
23 Oct 2004 | | Subject: | Dynamical Systems MSC-class: 37B05; 37A40 | math.DS | | Abstract: | For a Cantor set $X$, let $Homeo(X)$ denote the group of all homeomorphisms of $X$. The main result of this note is the following theorem. Let $Tin Homeo(X)$ be an aperiodic homeomorphism, let $mu_1,mu_2,...,mu_k$ be Borel probability measures on $X$, $e> 0$, and $n ge 2$. Then there exists a clopen set $Esubset X$ such that the sets $E,TE,..., T^{n-1}E$ are disjoint and $mu_i(Ecup TEcup...cup T^{n-1}E) > 1 - e, i= 1,...,k$. Several corollaries of this result are given. In particular, it is proved that for any aperiodic $Tin Homeo(X)$ the set of all homeomorphisms conjugate to $T$ is dense in the set of aperiodic homeomorphisms. | | Source: | arXiv, math.DS/0410505 | | Services: | Forum | Review | PDF | Favorites | |
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