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

TY - UNPB

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

AU - Thomsen, Klaus

N1 - Udkommer i Memoirs of the American Mathematical Society

PY - 2007

Y1 - 2007

N2 - We unify various constructions of -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 -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 -algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.

AB - We unify various constructions of -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 -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 -algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.

M3 - Working paper

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

PB - Department of Mathematical Sciences , University of Aarhus

CY - Århus

ER -