Introduction to Hyperbolic Dynamics and Ergodic Theory

These notes constitute an introductory text on dynamical systems centered on hyperbolic dynamics and ergodic theory whose numerous parts can be read independently. The first half presents the dynamics of hyperbolic sets: history, topological dynamics, ergodic theory, and invariant foliations. The second half introduces ergodic theory: ergodic theorems ergodic decomposition, recurrence, equidistribution, examples, mixing notions, correlation decay, and spectral isomorphism.