Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 1 
Assessment:  EX 100% 
Supplementary Assessment:  Likeforlike reassessment (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take MA20216 and take MA20217 and take MA20218 and take MA20219 and take MA20220 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. 
Programme availability: 
MA40045 is Optional on the following programmes:Department of Mathematical Sciences
