Markov Partitions and C-Diffeomorphisms

Among all diffeomorphisms,C-diffeomorphisms [sometimes also called U-diffeomorphisms ^* ] are distinguished by the maximum possible instability properties. Specifically, if T is a C-diffeomorphism of class C^r of some compact Riemannian manifold M of class C^∞, x∈M, then for any point x′ near x the distance between Tⁿx and Tⁿx′ increases with n at an exponential rate (either as n → +∞ or as n → −∞).