Noncommutative Geometry and Topology in Prague

Synchronizing Dynamical Systems

Expansive systems are a class of topological dynamical systems which exhibit sensitivity to initial conditions.  Following work by Klaus Thomsen, we will construct a C*-algebra from several different equivalence relations on the points in a given expansive system.  This generalizes the C*-algebraic construction made by Ian Putnam for Smale Spaces, which are themselves an important special case of expansive systems.  We will then present some results obtained for a type of expansive system called synchronizing systems, and we will compute K-theoretic invariants for some specific examples.  No knowledge of dynamical systems will be assumed for this talk.