Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

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

Simons Semester on Dynamics via YouTube

Overview

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.

Syllabus

Jonguk Yang (University of Zurich)

Taught by

Simons Semester on Dynamics

Reviews

Start your review of Infinite Renormalizability and Non-Uniform Partial Hyperbolicity in Two-Dimensional Dynamical Systems

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.