MT5877 - Ergodic Theory and Dynamical Systems - Spring 2026 - Preliminary

Welcome to the Ergodic Theory and Dynamical Systems (MT5877) course webpage. If you need any information that you can't find here, please email me. Chaotic dynamical systems are by definition difficult to analyse, and one of the most powerful approaches is to view the system through its associated measures (MT5865 is a prerequisite here - note any reference to MT5825 refers to a previous version of Measure Theory, which also works as a prerequisite here, but no longer runs). Then the system can be characterised via its average properties (with respect to that measure), its statistical limit laws (mixing properties, probabilistic theorems), as well as which measures the system supports. This course introduces dynamical systems and their associated measures and then covers basic recurrence theorems. There will also be an extensive discussion of entropy, which provides an important characterisation of the system (a measure of how chaotic the system is). The official description of this course is here.
Lecture: Wed, Fri, "Odd" Mon 11am-12pm in TBA
Tutorial: TBA

Contact Information

Lecturer: Mike Todd
Office: 320, Mathematical Institute
Email: m.todd -at- st-andrews.ac.uk
Course webpage: https://mtoddm.github.io/MT5877.html


Tutorial Sheets

The tutorial sheets are roughly weekly, see Moodle. You will have the opportunity for feedback on your work through the semester.
Announcements


Topics covered

  • Introduction to basic dynamical systems, examples
  • Poincaré Recurrence Theorem, Birkhoff's Ergodic Theorem, applications
  • Entropy of a measure preserving transformation, and applications (eg Kolmogorov Sinai Theorem)
  • The space of invariant measures


    Assessment

    100% by two hour examination


    Prerequisite

    MT5865 (i.e. you need to be able to work with Measure Theory)


    Textbooks

    The main textbook will be Walters' book. This and other useful books are listed below.
  • An Introduction to Ergodic Theory, Peter Walters, Springer
  • Ergodic Theory with a View Towards Number Theory, M. Einsiedler and T. Ward, Springer
  • Introduction to the modern theory of dynamical systems, A. Katok, B. Hasselblatt, Cambridge University Press, 1995
  • Ergodic Theory, K. Petersen, Cambridge University Press, 1983
  • Concepts and Results in Chaotic Dynamics, P. Collet and J.-P. Eckmann, Springer
  • Foundations of Ergodic Theory, M. Viana and K. Olivera, Cambridge University Press 2016