Markov partition

Summary

A Markov partition of a hyperbolic system is a cover of the space by finitely many pieces, called rectangles. The map moves these rectangles in a very regular way. Each rectangle is a product of a stable and an unstable piece, and the map stretches the unstable pieces across whole rectangles. Recording which rectangle a point visits at each time turns the system into a subshift of finite type. In this way Markov partitions make symbolic dynamics a tool for Anosov diffeomorphisms and for the basic sets of Axiom A systems.