## MAMCDTS-Dynamical Systems

Module Provider: Mathematics and Statistics
Number of credits: 12 [6 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites: MAMCDTU Data & Uncertainty MAMCDTE Partial Differential Equations
Modules excluded:
Module version for: 2016/7

Module Convenor: Dr Tobias Kuna

Summary module description:
Note: As this module is part of a joint programme with Imperial College London, the academic regulations for this module might differ from standard academic regulations usually applied at the University of Reading. The relevant document is the Joint Degree Programme Agreement between Imperial College London and University of Reading.

Aims:
This module develops the theoretical foundations of dynamical systems from a probabilistic viewpoint. A description of the long time or average behaviour of dynamical systems (deterministic or stochastic) is envisaged. This includes ergodic theory, large deviations and other limit theorems. Particular emphasis is on smooth dynamical systems, but the basic foundations taught will also cover general stationary stochastic processes.

Assessable learning outcomes:
On completion of this module students will have acquired:
• familiarity with a variety of mathematical techniques used in the theory of stochastic processes and dynamical systems such as ergodic theory, stationarity, invariant measures, attractors, ``nice'' invariant measures;
• quantitative measures of chaotic behaviour;
• limit theorems on various scales such as Central Limit Theorem and Large Deviation Principle.

Outline content:
Definitions and examples, Invariant measures, Perron Frobenius and spectral properties, Attractors, Axiom A systems, Ergodic theorem, Physical measures, Lyapunov exponents, KS entropy.

Brief description of teaching and learning methods:
Lectures and tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 6 Guided independent study 94 Total hours by term 120.00 Total hours for module 120.00

Summative Assessment Methods:
 Method Percentage Set exercise 50 Class test administered by School 50

Other information on summative assessment:

Formative assessment methods:
Peer marked tutorial questions

Penalties for late submission:

Where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Penalties for late submission on this module are in accordance with the University policy. Please refer to page 5 of the Postgraduate Guide to Assessment for further information: http://www.reading.ac.uk/internal/exams/student/exa-guidePG.aspx

Length of examination:

Requirements for a pass:
An average of 50% across the whole module.

Reassessment arrangements:
Via a written resit exam. Coursework will be carried forward if it received 40% or more, otherwise it must be resubmitted before the resit exam.