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C*-algebras of homoclinic and heteroclinic structure in expansive dynamics

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  • Department of Mathematical Sciences
We unify 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.
Original languageEnglish
Book seriesMemoirs of the American Mathematical Society
Volume206
Issue970
Pages (from-to)1-122
Number of pages122
ISSN0065-9266
DOIs
Publication statusPublished - 2010

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