Pesin theory

Summary

Pesin theory is the study of smooth dynamical systems that are hyperbolic only almost everywhere with respect to an invariant measure. Its starting point is the Oseledets theorem, which gives Lyapunov exponents at almost every point. When no exponent is zero, the theory builds local stable and unstable manifolds at almost every point. Their size and the angles between them may vary from point to point. It links the exponents with entropy, periodic orbits and the existence of physical measures.