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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1997, Volume 216, Pages 265–284 (Mi tm1011)  

This article is cited in 12 scientific papers (total in 12 papers)

Markov partitions and homoclinic points of algebraic $\mathbb Z^d$-actions

M. Einsiedler, K. Schmidt
Abstract: We prove that a general class of expansive $\mathbb Z^d$-actions by automorphisms of compact. Abelian groups with completely positive entropy has “symbolic covers” of equal topological entropy. These symbolic covers are constructed by using homoclinic points of these actions. For $d=1$ we adapt a result of Kenyon and Vershik in [7] to prove that these symbolic covers are, in fact, sofic shifts. For $d\ge2$ we are able t o prove the analogous statement only for certain examples, where the existence of such covers yields finitary isomorphisms between topologically nonisomorphic $\mathbb Z^2$-actions.
Received in March 1997
Bibliographic databases:
UDC: 517.9
Language: English
Citation: M. Einsiedler, K. Schmidt, “Markov partitions and homoclinic points of algebraic $\mathbb Z^d$-actions”, Dynamical systems and related topics, Collection of articles. To the 60th anniversary of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 216, Nauka, Moscow, 1997, 265–284; Proc. Steklov Inst. Math., 216 (1997), 259–279
Citation in format AMSBIB
\Bibitem{EinSch97}
\by M.~Einsiedler, K.~Schmidt
\paper Markov partitions and homoclinic points of algebraic $\mathbb Z^d$-actions
\inbook Dynamical systems and related topics
\bookinfo Collection of articles. To the 60th anniversary of academician Dmitrii Viktorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 1997
\vol 216
\pages 265--284
\publ Nauka
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm1011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1632169}
\zmath{https://zbmath.org/?q=an:0954.37008}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1997
\vol 216
\pages 259--279
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  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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