Introductory description

To study the long term behaviour of dynamical systems (or iterations of maps) using methods developed in Measure Theory, Linear Analysis and Probability Theory.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The contents covered in this module are:

• Measure preserving systems (with several examples)
• Ergodicity and notions of mixing
• The ergodic theorem and applications
• Entropy of measure preserving systems

Learning outcomes

By the end of the module, students should be able to:

• After taking this module, students will be familiar with the concept of measure preserving systems, the ergodic theorem, and the notion of entropy as a measure of unpredictability. Students will learn several examples of measure preserving systems and of connections between ergodic theory and other branches of mathematics.

Indicative reading list

A. Katok & B. Hasselblatt, Introduction to the modern theory of dynamical systems, C.U.P., 1995.

K. Petersen, Ergodic Theory, C.U.P., 1983.

P. Walters, An introduction to ergodic theory, Springer, 1982.

Subject specific skills

This module will equip students with several techniques to understand the long term behaviour of dynamical systems for a typical outcome. These skills can be applied to any situation where dynamical systems appear, which include many areas of engineering, meteorology, oceanography and biology.

Transferable skills

This module will equip students with several techniques to understand the long term behaviour of dynamical systems for a typical outcome. These skills can be applied to any situation where dynamical systems appear, which include many areas of engineering, meteorology, oceanography and biology.