Dynamical systems generated by ordinary differential equations and maps (MRI)

Credits	8 credit points
Instructors	Diekmann, O. (Universiteit Utrecht), Kuznetsov, Yu.A. (Universiteit Utrecht)
E-mail	O.Diekmann@uu.nl, I.A.Kouznetsov@uu.nl
Aim	The aim of this course is to introduce basic ideas, concepts, examples, results, techniques and methods for studying the orbit structure of dynamical systems on finite dimensional spaces generated by ODE (ordinary differential equations) (continuous time) or maps (discrete time).
Description	Subjects that will be treated in detail are : linearization near steady states : the Principle of Linearized Stability and local topological equivalence (the Grobman-Hartman Theorem) phase plane analysis : Poincare'-Bendixson theory, planar Hamiltonian systems from mechanics, predator-prey systems bifurcation theory (how does the orbit structure change when parameters are varied ?) for ODE and for maps stability of periodic solutions of ODE : Poincare' maps and Floquet multipliers Centre Manifold reduction the horseshoe map and symbolic dynamics (and chaotic behaviour)
Literature	Lecture notes will be provided. The course material includes pencil and paper exercises as well as exercises that require the use of sophisticated computer tools, such as CONTENT, see http://www.math.uu.nl/people/kuznet/CONTENT/ Training in the use of this tool is an integrated part of the course.

Last changed: 15-03-2012 15:37