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Department of Mathematical Sciences, Unit Catalogue 2010/11

MA40045: Dynamical systems

Click here for further information Credits: 6
Click here for further information Level: Masters
Click here for further information Period: This unit is available in...
Semester 1
Click here for further information Assessment: EX 100%
Click here for further informationSupplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Click here for further information 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
Click here for further information Description:
Aims & Learning Objectives:
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

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.