401-3372-00L Dynamical Systems II
|Semester||Spring Semester 2020|
|Language of instruction||English|
|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.
|Lecture notes||I will provide full lecture notes, available here:|
|Literature||The most useful textbook is|
- Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002.
|Prerequisites / Notice||It will be assumed you are familiar with the material from Dynamical Systems I. Full lecture notes for this course are available here:|
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.