Welcome

Ergodic theory has strong links to analysis, probability theory, (random and deterministic) dynamical systems, number theory, differential and difference equations and can be motivated from many different angles and applications. In contrast to topological dynamics, ergodic theory focusses on a probabilistic description of dynamical systems. Importantly, the "ergodic hypothesis" lies at the basis of statistical mechanics. A background in probability and measure  theory is required to understand even the basic material in ergodic theory. For this reason, the first part of the course will concentrate on a self-contained  review of the required background. The second part of the course will focus on selected topics in ergodic theory. 

The course is organised as a reading course leading to an individual project. There will be weekly meetings, where selected material will be presented and discussed within the group; this will guide the independent study. 

Recommended literature:

Martin Rasmussen, Ergodic Theory lecture notes (2017) as attached in the right-hand side margin.

Marcelo Viana and Krerley Oliveira. Foundations of Ergodic Theory (2016); full access online from Imperial at https://doi.org/10.1017/CBO9781316422601

Assessment:
M4 and MSc students can take this course for credit. Students taking the course for credit are to prepare an essay based on an individual project (counting for 60%); there will be a 30-minute oral exam on the project and the content of the course (counting for 40%). PhD students can also take this module for credit. Any interested PhD student is advised to discuss the method of assessment directly with me.