Memoirs of the American Mathematical Society 2010; 122 pp; softcover Volume: 206 ISBN10: 0821846922 ISBN13: 9780821846926 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/206/970
 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 onesided 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 1solenoids. For these dynamical systems it is shown that the \(C^*\)algebras are inductive limits of homogeneous or subhomogeneous algebras with onedimensional spectra. Table of Contents  The Ruelle algebra of a relatively expansive system
 On the functoriality of the Ruelle algebra
 The homoclinic algebra of expansive actions
 The heteroclinic algebra
 Onedimensional generalized solenoids
 The heteroclinic algebra of a group automorphism
 A dimension group for certain countable state Markov shifts
 Appendix A. Étale equivalence relations from abelian \(C^*\)subalgebras with the extension property
 Appendix B. On certain crossed product \(C^*\)algebras
 Appendix C. On an example of Bratteli, Jorgensen, Kim and Roush
 Bibliography
