Ergodic theory (Winter 2011)

Math 211B (Topics in Analysis)

     Course Code: 45525

MWF 1:00 – 1:50 pm, RH 440R

Final Exam: Wednesday, March 16, 1:30-3:30pm  

Instructor: Anton Gorodetski
        Email: asgor@uci.edu
        Phone: (949) 824-1381
        Office Location: RH 510G
        Office Hours: Monday 2-3pm or by appointment

 

 

 


Ergodic theory is the study of statistical properties of dynamical systems relative to a measure on the underlying space of the dynamical system. Or, in a broader way, it is the study of the qualitative properties of actions of groups on (measure) spaces. The word "ergodic" was introduce by Boltzman in the context of statistical mechanics, and is an amalgamation of the Greek words "ergon" (work) and "odos" (path). Currently ergodic theory is a fast growing field with numerous applications in different branches of mathematics.


This introductory course is aimed at advanced undergraduates, graduate students, physicists and other non-experts who may want to gain a basic understanding of the subject.

Notice that if you take a course in ergodic theory from two different instructors, most likely you will get two completely different courses, with different sets of topics, statements, and applications. This is due to the fact that the subject is relatively young, and has enormous amount of applications, generalizations, motivations, and ways to present. Besides classical results on recurrence, convergence of averages, entropy, and mixing properties, we will be interested mostly in the case when the phase space is equipped with some additional structure (topological or smooth), as well as in various applications (in number theory, mathematical physics, probability theory).

Recommended Texts:

  • P.Walters, An Introduction to Ergodic Theory, any edition.
  • M.Brin, G.Stuck,  Introduction to Dynamical Systems, Cambridge University Press, 2002.
  • A.Katok, B.Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, any edition.
  • P.R.Halmos, Ergodic Theory, any edition.
  • Ya.G.Sinai, Topics in Ergodic Theory, any edition.

Additional references will be given for a few topics not covered by these books.


Homework

 

Homework #1

Final Exam (due March 17)

 


 

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