$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics

Released on by Klaus Thomsen
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  • $C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics Book Detail

  • Author : Klaus Thomsen
  • Release Date : 2010-06-11
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 138
  • ISBN 13 : 0821846922
  • File Size : 29,29 MB
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$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics by Klaus Thomsen PDF Summary

Book Description: The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.

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