VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-3378-19L 8 Credits BSC , MSC D-MATH

Entropy in Dynamics

Lecturers & Examiners: Prof. Dr. Manfred Einsiedler
VVZ CR n/a

Last Updated: 2026-02-05 15:54:10

Abstract

Definition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Ergodic theorem for entropy. Topological entropy and variational principle. Measures of maximal entropy. Equidistribution of periodic points. Measure rigidity for commuting maps on the circle group.

Objective

The course will lead to a firm understanding of measure theoretic dynamical entropy and its applications within dynamics. We will start with the basic properties of (conditional) entropy, relate it to the question of effective coding techniques, discuss and prove the Shannon-McMillan-Breiman theorem that is also known as the ergodic theorem for entropy. Moreover, we will discuss a topological counter part and relate this topological entropy to the measure theoretic entropy by the variational principle. We will use these methods to classify certain natural homogeneous measures, prove equidistribution of periodic points on compact quotients of hyperbolic surfaces, and establish a measure rigidity theorem for commuting maps on the circle group.

Resources

Lecture Notes

Entropy book under construction, available online underhttps://tbward0.wixsite.com/books/entropy

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
session examination
Mode
oral 20 minutes
20 minutes preparation and 20 minutes exam (one candidate prepares during the 20 minutes oral exam of the previous candidate). The exam is only offered in the examination sessions Summer 2021 and Winter 2022.The active participation in the exercise class via presentations as a voluntary learning task will be graded and can improve the total course unit grade by up to 0.25 grade points. Students can still achieve the maximum grade of 6 in the course unit even if they only sit the final examination.

Course Components

Type Title Time & Place Hours
lecture with exercise Entropy in Dynamics
continues to take place online via Zoom till the end of the semester
  • Wed 14:15-16:00 (HG E 1.1)
  • Fri 10:15-12:00 (HG G 26.5)
4 h weekly

Offered In