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401-3372-00L 10 Credits BSC , MSC D-MATH

Dynamical Systems II

Lecturers & Examiners: Dr. Will Merry
VVZ CR n/a

Last Updated: 2026-02-05 15:41:21

Abstract

This course is a continuation of Dynamical Systems I. This time the emphasis is on hyperbolic and complex dynamics.

Objective

Mastery of the basic methods and principal themes of some aspects of hyperbolic and complex dynamical systems.

Content

Topics covered include: - Hyperbolic linear dynamical systems, hyperbolic fixed points, the Hartman-Grobman Theorem. - Hyperbolic sets, Anosov diffeomorphisms. - The (Un)stable Manifold Theorem. - Shadowing Lemmas and stability. - The Lambda Lemma. - Transverse homoclinic points, horseshoes, and chaos. - Complex dynamics of rational maps on the Riemann sphere - Julia sets and Fatou sets. - Fractals and the Mandelbrot set.

Resources

Lecture Notes

I will provide full lecture notes, available here:https://www.merry.io/courses/dynamical-systems/

Literature

The most useful textbook is - Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002.

General Information

Language
English
Levels
BSC , MSC

Examination

Type
session examination
Mode
written 180 minutes
Aids
None
Offered in the summer examination session 2020 and in the winter examination session 2020/21. Be aware that no further examination might be offered until this non-recurring course will be offered again.

Course Components

Type Title Time & Place Hours
lecture Dynamical Systems II
  • Tue 15:15-17:00 (HG D 1.2)
  • Fri 10:15-12:00 (HG D 1.2)
4 h weekly
exercise Dynamical Systems II
  • Fri 12:15-13:00 (HG D 1.2)
1 h weekly

Offered In