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401-5262-DRL 2 Credits DR D-MATH

Ergodic Theory of Surface Diffeomorphisms

Lecturers & Examiners: PD Dr. Sylvain Félix Crovisier
Doctoral students of I-Math (UZH) need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-06-03 00:14:17

Abstract

Nachdiplom lecture

Content

We propose to present recent advances in the study of the dynamics of non-uniformly hyperbolic diffeomorphisms, with a particular focus on the two-dimensional case. The dynamics of uniformly hyperbolic dynamical systems have been well understood since the 70’s (after Anosov, Smale, Sinai, Ruelle, Bowen,…): these systems are structurally stable under perturbations, they decompose into finitely many invariant basic pieces that can be studied separately, they exhibit well-described statistical behavior through classical limit theorems. Another classical tool for differentiable dynamics - Pesin theory - describes the geometric properties of any invariant probability measure which satisfies a non-uniformly hyperbolicity. These lectures will explore the non-uniformly hyperbolic set of a differentiable dynamical system: in dimension two, this set supports all the part of the dynamics which exhibits enough complexity - namely, which has positive entropy. We will discuss several techniques developed over the past fifteen years, including decomposition into Borel homoclinic classes, coding and reduction to a symbolic setting, high regularity rigidity from Yomdin theory. Although the decomposition may involve infinitely many pieces, we will explain how its complexity can be controlled by dynamical invariants such as entropy and Lyapunov exponents. Under suitable smoothness and expansion assumptions, we will see that most of the orbits equidistribute towards natural invariant measures (physical or maximizing the entropy), and satisfy statistical limit theorems.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Course Components

Type Title Time & Place Hours
lecture Ergodic Theory of Surface Diffeomorphisms
If you would like to attend the lecture, please register by 25 February. For the registration form see
  • Thu 10:15-12:00 (HG G 43)
2 h weekly

Offered In