Infinite Renormalizability and Non-Uniform Partial Hyperbolicity in Two-Dimensional Dynamical Systems

Explore the concept of infinite renormalizability and non-uniform partial hyperbolicity in dynamical systems through this 56-minute lecture by Jonguk Yang from the University of Zurich. Delve into the generalization of renormalization theory from one-dimensional unimodal interval maps to a two-dimensional setting, including real Hénon maps. Discover how identifying the appropriate notion of a "critical point" using a quantitative reformulation of Pesin theory allows for an explicit description of non-uniform partial hyperbolicity in infinitely renormalizable "unimodal" diffeomorphisms. Learn about the main result of a priori bounds for these systems, providing uniform control on the dynamics' geometry at arbitrarily small scales. Gain insights into this joint work with S. Crovisier, M. Lyubich, and E. Pujals, presented as part of the Simons Semester on Dynamics.