SUBJECT
Title
Dynamics in one complex variable
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Julia és Fatou sets. Smooth Julia sets. Attractive fixpoints, Koenigs linearization theorem. Superattractive fixpoints Bötkher theorem. Parabolic fixpoints, Leau-Fatou theorem. Cremer points és Siegel discs. Holomorphic fixpoint formula. Dense subsets of the Julia set.. Herman rings. Wandering domains. Iteration of Polynomials. The Mandelbrot set. Root finding by iteration. Hyperbolic mapping. Local connectivity.
Readings
- John Milnor: Dynamics in one complex variable, Stony Brook IMS Preprint #1990/5
Further reading:
- M. Yu. Lyubich: The dynamics of rational transforms, Russian Math Survey, 41 (1986) 43–117
- A. Douady: Systeme dynamique holomorphes, Sem Bourbaki , Vol 1982/83, 39-63, Asterisque, 105–106