401-3372-00L  Dynamical Systems II

SemesterSpring Semester 2020
LecturersW. Merry
Periodicitynon-recurring course
Language of instructionEnglish


AbstractThis course is a continuation of Dynamical Systems I. This time the emphasis is on hyperbolic and complex dynamics.
ObjectiveMastery of the basic methods and principal themes of some aspects of hyperbolic and complex dynamical systems.
ContentTopics 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.
Lecture notesI will provide full lecture notes, available here:

Link
LiteratureThe most useful textbook is

- Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002.
Prerequisites / NoticeIt will be assumed you are familiar with the material from Dynamical Systems I. Full lecture notes for this course are available here:

Link

However we will only really use material covered in the first 10 lectures of Dynamical Systems I, so if you did not attend Dynamical Systems I, it is sufficient to read through the notes from the first 10 lectures.

In addition, it would be useful to have some familiarity with basic differential geometry and complex analysis.