Programme & Unit Catalogues - University of Bath

Department of Mathematical Sciences, Unit Catalogue 2009/10

MA40045: Dynamical systems

Credits:

Level:

Masters

Period:

Semester 1

Assessment:

EX 100%

Supplementary Assessment:

Like-for-like reassessment (where allowed by programme regulations)

Requisites:

Before taking this unit you must take MA20007 and take MA20008 and take MA20009 and take MA20011 and take MA20012 and take MA30041 and take MA40062

Description:

Aims & Learning Objectives:
Aims:
A treatment of the qualitative/geometric theory of dynamical systems to a level that will make accessible an area of mathematics (and allied disciplines) that is highly active and rapidly expanding.
Objectives: Conversance with concepts, results and techniques fundamental to the study of qualitative behaviour of dynamical systems. An ability to investigate stability of equilibria and periodic orbits. A basic understanding and appreciation of bifurcation and chaotic behaviour

Content:
Topics will be chosen from the following: Stability of equilibria. Lyapunov functions. Invariance principle. Periodic orbits. Poincaré maps. Hyperbolic equilibria and orbits. Stable and unstable manifolds. Nonhyperbolic equilibria and orbits. Centre manifolds. Bifurcation from a simple eigenvalue. Introductory treatment of chaotic behaviour. Horseshoe maps. Symbolic dynamics.

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.