Remote access

How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2294  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax

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

About this Title

Klaus Thomsen, IMF, Ny Munkegade, 8000 Aarhus C, Denmark

Publication: Memoirs of the American Mathematical Society
Publication Year: 2010; Volume 206, Number 970
ISBNs: 978-0-8218-4692-6 (print); 978-1-4704-0584-7 (online)
Published electronically: February 24, 2010
MathSciNet review: 2667385
MSC: Primary 46L55; Secondary 37B10, 37D20, 46L05, 46L35, 46L80

View full volume PDF

View other years and numbers:

Table of Contents


  • Chapter 1. The Ruelle algebra of a relatively expansive system
  • Chapter 2. On the functoriality of the Ruelle algebra
  • Chapter 3. The homoclinic algebra of expansive actions
  • Chapter 4. The heteroclinic algebra
  • Chapter 5. One-dimensional generalized solenoids
  • Chapter 6. The heteroclinic algebra of a group automorphism
  • Chapter 7. 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


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.

References [Enhancements On Off] (What's this?)