Overview
Explore the first lecture in a mini-course series that delves into extending renormalization theory from one-dimensional to two-dimensional dynamical systems. Learn how self-similarity at smaller scales can reveal crucial insights about combinatorial, topological, and geometric aspects of dynamics. Discover how the theory of non-uniformly partially hyperbolic systems combines with renormalization approaches to generalize unimodal interval maps to diffeomorphisms in dimension two. Master key concepts including the higher-dimensional analog of critical points, two-dimensional a priori bounds, and uniform control of dynamics at small scales. Study the proof of a priori bounds for unimodal interval maps, quantitative Pesin theory, critical orbit definition in 2D, linear ordering on renormalization limit sets, and the regularity of first return maps.
Syllabus
Jonguk Yang (University of Zurich), lecture 1b
Taught by
Simons Semester on Dynamics