Nonstandard Functional Central Limit Theorem for Nonuniformly Hyperbolic Dynamical Systems, Including Billiards and Geodesic Flows

Explore the nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems in this 52-minute conference lecture from the 8th Brazilian School of Dynamical Systems. Delve into advanced mathematical concepts as Ian Melbourne from the University of Warwick presents his research on billiards and geodesic flows within the context of dynamical systems theory. Learn about the theoretical foundations and applications of functional central limit theorems when applied to systems that exhibit nonuniform hyperbolicity, a key property in modern dynamical systems research. Examine how these mathematical frameworks apply to specific examples including billiard systems and geodesic flows on manifolds. Gain insights into cutting-edge research in ergodic theory and probability theory as they intersect with dynamical systems. This presentation is part of a prestigious Brazilian academic event that brings together postgraduate students and researchers in dynamical systems, ergodic theory, and related fields including geometry, probability, number theory, and topology, fostering international academic collaboration and knowledge exchange in these mathematical disciplines.