Dynamical Systems

Below is a list of reviews of books on dynamical systems.

Introduction to Dynamical Systems
Brin, M., Stuck, G. (2015). ISBN 9781107538948.
Prerequisites: Point-Set Topology, Analysis, and Basic Measure Theory

A concise but thorough introduction to Dynamical Systems through the lens of actions on sets. The text focuses largely on topological dynamics and measurable dynamics, as well as their intersection with Borel measures.

Ergodic Theory and Dynamical Systems
Coudène, Y. (2016). ISBN 9781447172857
Prerequisites: Topology, measure theory and functional analysis required. Basics of smooth manifolds and complex analysis are helpful.\

This book introduces the core theorems in ergodic theory, topological dynamics, and dynamical entropy, emphasizing chaotic dynamics. It is concise but well-written, with clean proofs, good pictures, and a handful of exercises after each chapter. Coudène is excellent for examples, including a study of geodesic flows on negatively-curved spaces, rational maps on the Riemann sphere, information theoretic examples, and strange attractors.