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

TY - JOUR

T1 - C*-algebras of homoclinic and heteroclinic structure in expansive dynamics

AU - Thomsen, Klaus

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

U2 - 10.1090/S0065-9266-10-00581-8

DO - 10.1090/S0065-9266-10-00581-8

M3 - Journal article

SN - 0065-9266

VL - 206

SP - 1

EP - 122

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 970

ER -