401-3372-00L Dynamical Systems II
|Semester||Spring Semester 2017|
|Language of instruction||English|
|Abstract||This course is a continuation of Dynamical Systems I. This time the emphasis is on hyperbolic dynamics.|
|Objective||Mastery of the basic methods and principal themes of some aspects of hyperbolic dynamical systems.|
|Content||Topics covered include:|
- Circle homeomorphisms and rotation numbers.
- 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.
|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.
Another (more advanced) useful book is
- Introduction to the Modern Theory of Dynamical Systems, Katok and Hasselblatt, CUP, 1995.
|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 12 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 12 lectures.
In addition, it would be useful to have some familiarity with basic differential geometry.