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C*-algebras of homoclinic and heteroclinic structure in expansive dynamics / Klaus Thomsen.
- Format:
- Book
- Author/Creator:
- Thomsen, Klaus, 1957- author.
- Series:
- Memoirs of the American Mathematical Society ; Volume 206, Number 970.
- Memoirs of the American Mathematical Society, 0065-9266 ; Volume 206, Number 970
- Language:
- English
- Subjects (All):
- C*-algebras.
- Dynamics.
- Physical Description:
- 1 online resource (122 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 2010.
- Language Note:
- English
- Summary:
- 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 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.
- Contents:
- ""Chapter 4. The heteroclinic algebra""""4.1. Post-periodic points and the Wagoner topology""; ""4.2. Functoriality of the post-periodic points and the Wagoner topology""; ""4.3. The heteroclinic algebra of a countable state Markov shift""; ""4.4. The heteroclinic algebra of a Smale space""; ""4.5. More inductive limit decompositions""; ""Chapter 5. One-dimensional generalized solenoids""; ""5.1. Mixing 1-solenoids""; ""5.2. On the structure of the heteroclinic algebra""; ""Chapter 6. The heteroclinic algebra of a group automorphism""
- ""Appendix C. On an example of Bratteli, Jorgensen, Kim and Roush""""Bibliography""
- Notes:
- "Volume 206, Number 970 (end of volume)."
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 1-4704-0584-9
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