[Alex Furman]
[CV]
[Research]
Math 546 Ergodic Theory, Spring 2009
General Information
Math 546, Call #26336, Spring 2009
Classes: MWF at 9-9:50 am in 215 TH at 1-1:50pm in 612 SEO
Instructor: Alex Furman
Office hours: by appointment
Contact: furman AT math DOT uic DOT edu
Text: Karl Petersen "Ergodic Theory" (Cambridge Studies in Advanced Mathematics).
Prerequisites: Measure and Integration (as in Math 533 Real Analysis).
Syllabus (tentative)
Part I - Basic Theory :
examples, ergodic theorems (von Neumann, Birkhoff,
Kingman, Oseledets x 2), notions of mixing, weak mixing, discrete spectrum;
uniquely ergodic systems.
Part II - Entropy:
Kolomogorov-Sinai entropy, topological entropy, variational principle, Pesin formula,
Shannon-McMillan-Breiman theorem, some symbolic dynamics.
Part III - Applications: Furstenberg's proof of Szemeredi theorem.
Announcements
- Time changed to 1-1:50pm. Place changed to 612 SEO
- Final projects: choose one out of four suggested projects
Further Reading
[Alex Furman]
[CV]
[Research]