Entry requirements

Algebra MN1, Analysis MN2, Fourier analysis MN1,

Complex analysis MN1 and Introduction to

scientific programming MN1. The course Real

analysis MN1 facilitates the understanding of

the course.

Aims

An introduction to dynamical systems, in particular to stability theory and chaotic phenomena.

Content

The course gives an introduction to the theory

of dynamical systems with an emphasise on

stability properties of systems, the dependency

on parameters and chaotic phenomena. The

following items are treated. Autonomous systems

of differential equations, phase portraits.

Asymptotic stability and Lyapunov functions.

Interval mappings, chaos and sensitive

dependence on initial data. Conjugation,

structural stability and symbolic dynamics.

Differential equations on the torus and circle

mappings. Basic bifurcation theory. Higher

dimensional mappings, stable and unstable

manifold, hyperbolicity. Briefly about complex

dynamical systems. Computer simulations.

Instruction

Lectures, problem solving sessions and computer

laboratory sessions.

Assessment

Written and, possibly, supplementary oral

examination at the end of the course. Moreover,

compulsory assignments may be given during the

course.