MT5877 Ergodic Theory and Dynamical Systems

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11am Mon (weeks 1, 3, 5, 7, 9, 12), Wed & Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof M J Todd

Prof M J Todd
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Prof Mike Todd

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module introduces the modern ergodic theory approach to understanding chaotic dynamical systems. Topics include recurrence, consequences of ergodicity, entropy, the structure of the space of invariant measures and unique ergodicity. This will give students an insight into a thriving field of mathematics, which is at the core of the research interests of many faculty in the Pure Division in the School of Mathematics and Statistics.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT5865 OR PASS MT5825

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE MT5837

Assessment pattern

2-hour written examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (weeks 1-10), 1 tutorial (weeks 2-11)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

117

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Be able to work with some simple dynamical system models
  • Understand how invariant measures can be used to explain the recurrence properties of a dynamical system
  • Appreciate ergodicity: as a building block for understanding all the average behaviours of a system, and the classical theorems (e.g. Birkhoff's Ergodic Theorem) associated to it
  • Be able to define, work with and develop an intuitive understanding of, entropy
  • Understand the fundamental structure of the set of invariant measures