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

YouTube

Renormalization Theory in Two-Dimensional Dynamical Systems - Lecture 2A

Simons Semester on Dynamics via YouTube

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Learn about renormalization theory in higher dimensions through this mathematics lecture that explores the extension of one-dimensional techniques to two-dimensional dynamical systems. Discover how combining renormalization approaches with non-uniformly partially hyperbolic systems theory enables the analysis of diffeomorphisms in dimension two. Explore key concepts including the identification of higher-dimensional critical points, two-dimensional a priori bounds, and uniform control of dynamics at small scales. Examine topics like quantitative Pesin theory, critical orbits in 2D, linear ordering on renormalization limit sets, and the regularity of first return maps. Gain insights from research conducted jointly with S. Crovisier, M. Lyubich and E. Pujals that bridges fundamental concepts from one-dimensional unimodal interval maps to more complex two-dimensional systems.

Syllabus

Introduction
L regularity
Percent regularity
Boundary of chaos
Fagen bound
Critical orbit
quadratic critical orbit
unit model

Taught by

Simons Semester on Dynamics

Reviews

Start your review of Renormalization Theory in Two-Dimensional Dynamical Systems - Lecture 2A

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.