Preface ....................................................... vii
Chapter 1. The Ruelle algebra of a relatively expansive
system ..................................................... 1
1.1. Relatively expansive systems ............................... 1
1.2. The etale equivalence relation of local conjugacy .......... 2
1.3. The C*-algebra of a local conjugacy relation ............... 8
1.4. Products and unions ....................................... 10
Chapter 2. On the functoriality of the Ruelle algebra .......... 13
2.1. Contravariant functoriality ............................... 13
2.2. Covariant functoriality ................................... 16
Chapter 3. The homoclinic algebra of expansive actions ......... 23
3.1. Shift spaces .............................................. 23
3.2. Expansive actions by affine maps .......................... 28
3.3. Expansive group automorphisms ............................. 34
Chapter 4. The heteroclinic algebra ............................ 41
4.1. Post-periodic points and the Wagoner topology ............. 41
4.2. Functoriality of the post-periodic points and
the Wagoner topology ...................................... 46
4.3. The heteroclinic algebra of a countable state Markov
shift ..................................................... 47
4.4. The heteroclinic algebra of a Smale space ................. 50
4.5. More inductive limit decompositions ....................... 53
Chapter 5. One-dimensional generalized solenoids ............... 57
5.1. Mixing 1-solenoids ........................................ 57
5.2. On the structure of the heteroclinic algebra .............. 61
Chapter 6. The heteroclinic algebra of a group automorphism .... 67
6.1. Automorphisms locally expansive on post-periodic points ... 67
6.2. The heteroclinic algebra of an expansive automorphism
of a compact group ........................................ 70
6.3. The homoclinic algebra of an expansive group
automorphism .............................................. 81
Chapter 7. A dimension group for certain countable state
Markov shifts ............................................. 83
7.1. Markov shifts with finitely many edge-disjoint
doublepaths ............................................... 83
7.2. The structure of the heteroclinic algebra ................. 99
Appendix A. Ėtale equivalence relations from abelian
C*-subalgebras with the extension property ............... 103
Appendix B. On certain crossed product C*-algebras ............ 109
Appendix C. On an example of Bratteli, Lorgensen, Kim and
Roush .................................................... 115
Bibliography .................................................. 119
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