Pesin's Theorem is a fundamental result in ergodic theory that establishes a connection between the existence of measure-theoretic entropy and the presence of stable and unstable manifolds for dynamical systems. This theorem highlights the relationship between the chaotic behavior of a system and its underlying geometric structure, especially in the context of hyperbolic systems. It plays a critical role in understanding the behavior of systems with positive Lyapunov exponents.
congrats on reading the definition of Pesin's Theorem. now let's actually learn it.