Entry requirements

Mathematics, 90 ECTS credits including Complex

analysis MN1 and Fourier analysis MN1.

Aims

The course gives basic knowledge in complex dynamics which is

presently

one of the very active and popular subjects of mathematics.

Content

Iterations of analytic functions of one complex

variable, in particular of rational functions.

Classification of fixed points and conjugation for

analytic functions

of one variable, one-dimensional rational iteration,

Julia and Fatou

sets, Sullivan's classification of Fatou components,

Siegel discs and

Herman rings, quadratic polynomials and the Mandelbrot

set.

Instruction

Lectures and problem solving sessions.

Assessment

Oral exam.