In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction". Anosov systems are a special case of Axiom A systems.
Anosov diffeomorphisms were introduced by Dmitri Victorovich Anosov, who proved that their behaviour was in an appropriate sense generic (when they exist at all).[1]