Explore a mathematics lecture from the Centre International de Rencontres Mathématiques that delves into measuring complexity in dynamical systems, specifically focusing on arithmetic dynamics through topological, algebraic, and arithmetic perspectives. Learn about dynamical degrees as an algebraic analog to entropy and their application in studying orbits, periodic points, and cohomology actions. Recorded during the "Arithmetic, Algebraic and Analytics Dynamics" thematic meeting in Marseille, France, this 90-minute presentation is available through CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched content with abstracts and bibliographies, and comprehensive Mathematics Subject Classification tags for enhanced navigation and learning.