MTH5118 · Dynamical systems

Overview

The field of dynamical systems uses tools from topology and geometry to study systems that change over time and their long-term behaviour. It has applications in physics, chemistry, biology, computer science and economics. This unit will cover fundamental results in dynamical systems and introduce classical examples, stable and unstable manifold theory, uniform hyperbolicity, and other geometric tools. It will also cover basic techniques for numerically analysing dynamical systems.

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Identify and analyse different types of dynamical behaviour, both chaotic and non-chaotic;
2. Prove results about dynamical systems using topological arguments and reasoning;
3. Investigate dynamical systems using numerical methods on a computer;
4. Apply dynamical systems theory to other areas of mathematics and the sciences;
5. Communicate mathematical ideas relating to dynamical systems in a clear, precise and rigorous manner.

Workload

• Three hours of seminars; • One hours of applied sessions and • Eight hours of independent study per week

Student experience, not official rules. Nothing here changes what the Handbook says.