YoVDO

Continuity Properties of Lyapunov Exponents - Lecture 7

Offered By: Simons Semester on Dynamics via YouTube

Tags

Dynamical Systems Courses Entropy Courses Measure Theory Courses Lyapunov Exponents Courses Spectral Gap Courses Surface Diffeomorphisms Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore the continuity properties of Lyapunov exponents in this lecture from the Simons Semester on Dynamics series. Delve into the control of Lyapunov exponents using entropy for smooth surface diffeomorphisms, based on recent joint works with Sylvain Crovisier and Omri Sarig. Learn about computing the entropy of measures through the expansion of smooth unstable curves using Yomdin's reparametrization technique. Understand the relationship between potential drops in Lyapunov exponents and "near" homoclinic tangencies, which impede the expansion of unstable curves over extended time periods. Gain insights into fundamental concepts in smooth ergodic theory, followed by an examination of key estimates and a discussion of the main result. Time permitting, discover the consequences of this result, including a spectral gap property for entropy-maximizing measures, and explore the construction of Sinai-Ruelle-Bowen measures using these methods.

Syllabus

Jérôme Buzzi (Université Paris-Saclay), lecture 7


Taught by

Simons Semester on Dynamics

Related Courses

Measure Theory
NPTEL via Swayam
Measure Theory - IITB
NPTEL via Swayam
Measure Theory - IMSc
IMSC via Swayam
Quantum Theory
Friedrich–Alexander University Erlangen–Nürnberg via YouTube
Measure and Integration
IMSC via Swayam