Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties

Explore the dynamics of smooth surface diffeomorphisms in this comprehensive lecture by Omri Sarig from Weizman, Israel. Delve into topics such as spectral gap and stochastic properties, beginning with a recap of exponential degree of correlations and the stronghold variance principle. Examine the central limit theorem and the law of iterated logarithm before diving into symbolic models and passing sets. Investigate optimal pressing constants, geometric potentials, and entropy continuity. Analyze spectral properties and the existence of spectral gaps, learning how to determine if a given matrix admits a space with specific properties. Study countable Markov shifts, the binology of hyperbolas, and escape to infinity. Conclude with insights into entropy at infinity and symbolic dynamical results in this 1 hour and 23 minute presentation from the ICTP Mathematics series.

Introduction
Recap
Exponential degree of correlations
The stronghold variance principle
Central limit theorem
Law of iterated logarithm
Symbolic model
Passing sets
Optimal pressing constant
Geometric potential
Entropy continuity
Symbolic dynamics
Spectral properties
Spectral gap property
Does spectral gap exist
How to decide whether a given matrix admits about a space with all those properties
Countable markov shifts
Binology of hyperbolas
Escape to infinity
entropy at infinity
symbolic dynamical result
conclusion