# Dynamics of piecewise contraction maps

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Our talk is concerned with the study of dynamical systems which are piecewise contraction maps (PC maps). Certain mathematical models, like contracting outer billi- ards and switched flow systems, are described by PC maps. In the setup, one considers a convex subset X ⊂ Rd and a finite partition of X: X1,...,Xn. Then the map f : X → X is assumed to be a contraction on each element Xi of the partition. It is expected that a typical PC map has finitely many periodic orbits and every orbit converges to a periodic orbit.