401-3371-00L  Dynamical Systems I

SemesterAutumn Semester 2015
LecturersW. Merry
Periodicitynon-recurring course
Language of instructionEnglish


AbstractThis course is a Part I of a broad introduction to dynamical systems. Topic covered include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics. In Part II (FS 2016), we will cover low-dimensional dynamics, complex dynamics, measure-theoretic entropy and Hamiltonian dynamics.
ObjectiveMastery of the basic methods and principal themes of dynamical systems.
ContentThe course introduces the principal themes of modern dynamical systems. Topics covered include:

1. Topological dynamics
(transitivity, attractors, chaos, structural stability)

2. Symbolic dynamics
(Perron-Frobenius theorem, zeta functions)

3. Ergodic theory
(Poincare recurrence theorem, Birkhoff ergodic theorem, existence of invariant measures)

4. Hyperbolic dynamics
(Grobman-Hartman theorem, Shadowing lemma, Closing lemma and applications)
LiteratureThe most relevant textbook for this course is

Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002.

Another excellent book (which will be relevant also for Dynamical Systems II) is

Lectures on Dynamical Systems, Zehnder, EMS 2010.

A more advanced textbook which covers everything in both Dynamical Systems I and II (and much more!) is

Introduction to the Modern Theory of Dynamical Systems, Katok and Hasselblatt, CUP, 1995.
Prerequisites / NoticeThe material of the basic courses of the first two years of the program at ETH is assumed. Some basic differential geometry and functional analysis would be useful but not essential.