This course covers the dynamics of smooth surface diffeomorphisms, focusing on spectral gap and stochastic properties. The learning outcomes include understanding exponential degree of correlations, the central limit theorem, symbolic dynamics, spectral properties, and spectral gap property. The course teaches skills such as analyzing countable Markov shifts, studying the binology of hyperbolas, and exploring entropy at infinity. The teaching method involves theoretical explanations and mathematical proofs. This course is intended for individuals interested in advanced topics in mathematics, particularly in dynamical systems and spectral theory.
Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties
Overview
Syllabus
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
Taught by
ICTP Mathematics
