Geometry, Dynamics, and Rigidity

A generously illustrated textbook and reference for graduate students and researchers that integrates two major areas of mathematicsGeometry, Dynamics, and Rigidity is an introduction to the modern interface between Riemannian geometry and dynamical systems. Organized in three parts, the book builds the geometric and analytic background (“Geometry”), develops the core machinery of hyperbolic dynamics (“Dynamics”), and then assembles these tools to prove three landmark rigidity theorems (“Rigidity”).Amie Wilkinson’s informal yet precise and detailed exposition balances approachability with depth: definitions and motivations appear where they are first needed, proofs are complete and carefully structured, and historical notes connect classical ideas to current research. Designed for beginning graduate students as well as researchers entering from either side of the subject, the text emphasizes concepts-including geodesic flows, curvature and entropy, Anosov and related systems, and invar