We study the hyperbolic dynamical systems known as Smale spaces. More specifically
we investigate the C*-algebras constructed from these systems. The K group
of one of these algebras has a natural ring structure arising from an asymptotically
abelian property. The K groups of the other algebras are then modules over this
ring. In the case of a shift of finite type we compute these structures explicitly and
show that the stable and unstable algebras exhibit a certain type of duality as modules.
We also investigate the Bowen measure and its stable and unstable components
with respect to resolving factor maps, and prove several results about the traces that
arise as integration against these measures. Specifically we show that the trace is
a ring/module homomorphism into R and prove a result relating these integration
traces to an asymptotic of the usual trace of an operator on a Hilbert space.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/1564 |
| Date | 24 August 2009 |
| Creators | Killough, D. Brady |
| Contributors | Putnam, Ian Fraser |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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