A homology theory for Smale spaces: a summary

Details A homology theory for Smale spaces: a summary A homology theory for Smale spaces: a summary

2008-01-22

arxiv.org/abs/0801.3294v2

Mathematics

Dynamical Systems

Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definitio

Scientific paper

We consider Smale spaces, a particular class of hyperbolic topological dynamical systems, which include the basic sets for Smale's Axiom A systems. We present a homology theory for such systems which is based on the dimension group in the special case of shifts of finite type. This theory provides a Lefschetz formula relating trace data with the number of periodic points of the system.

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