Introduction to dynamical systems (BM)

Vakbeschrijving Introduction to dynamical systems (BM)
Collegejaar: 2017-2018
Studiegidsnummer: 4373INTDS
Docent(en):
  • prof.dr. A. Doelman
Voertaal: Engels
Blackboard: Nee
EC: 6
Niveau: 400
Periode: Semester 1
  • Wel Keuzevak
  • Wel Contractonderwijs
  • Wel Exchange
  • Wel Study Abroad
  • Geen Avondonderwijs
  • Wel A-la-Carte en Aanschuifonderwijs
  • Geen Honours Class

Description

There are various kinds of dynamical systems: discrete maps, smooth, finite dimensional, ordinary differential equations, and infinite dimensional systems such as partial, functional or stochastic differential equations. This introductory course focuses on the second type, dynamical systems generated by ordinary differential equations. However, the ideas developed in this course are central to all types of dynamical systems. First, some fundamental concepts — asymptotic stability by linearization, topological conjugacy, omega-limit sets, Poincar\é maps — are introduced, building on a basic background in the field of ordinary differential equations. Next, the existence and character of invariant manifolds — that play an essential role in the theory of dynamical systems — will be considered. This will give a starting point for the study of bifurcations.

The field of dynamical systems is driven by the interplay between pure’ mathematics and explicit questions and insights fromapplications’ — ranging from (classical) physics and astronomy to ecology and neurophysiology. This is also reflected in the way this course will be taught: it will be a combination of developing mathematical theory and working out explicit example systems.

Remarks

This course can be seen as a basic ingredient of the program chosen by a student who intends to specialize on analysis. However, it also is a relevant subject for students whose main interests lie in geometry, stochastics or numerical mathematics.

More explicitly, this course can be seen as a natural preparation for the courses Introduction to Perturbation Methods’,Bifurcations and Chaos’, and several national master courses (such as `Partial Differential Equations’).

Examination

Handing in assignments

Prerequisites

Ordinary differential equations.

Literature

Compulsory: Differential Dynamical Systems (Monographs on Mathematical Modeling and Computation 1), James D. Meiss, SIAM, 434 pp, ISBN 0898716357 – ISBN-13 9780898716351

Talen