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 University | Catalogues for 2006/07

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Department of Mathematical Sciences, Unit Catalogue 2006/07

MA40045 Dynamical systems

Credits: 6
Level: Masters
Semester: 1
Assessment: EX 100%
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

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
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.


University | Catalogues for 2006/07