This lecture, part of a series on the ergodic theory of geodesic flows on hyperbolic surfaces, explores the chaotic behavior of these mathematical systems. Delve into the construction of invariant measures known as "Gibbs measures" and learn how their product structure reveals chaotic properties of the flow. Discover how this family of measures can yield elegant geometric results. Recorded during the thematic meeting "Geometric structures and discrete group actions" on April 15, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other mathematical talks on CIRM's Audiovisual Mathematics Library, featuring helpful tools like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search functionality.