Ergodic Theory: Math 646

Meeting : TuTh 1:00    TBA

Instructor : Luc Rey-Bellet

 Office :  1423 J LGRT
 Phone :  545-6020
 E-Mail :  luc@math.umass.edu
 Office Hours :   Tuesday 2:45--4:00,   Thursday 2:45--4:00,   or by appointment.

Text: The text is Walter's " An introduction to ergodic theory".

References

• An introduction to ergodic theory, by Peter Walters, Graduate Texts in Mathematics, Springer.
  
  
• Ergodic Theory, by Karl Petersen, Cambridge University Press.
  
  
• Ergodic theory and differentiable dynamics, by Ricardo Mane, Springer.
  
  
• Introduction to ergodic theory, by Ya. G. Sinai, Princeton University Press.
  
  
• Topics in ergodic theory, by Ya. G. Sinai, Princeton University Press.
  
  
• Ergodic theory, by I.P Cornfeld, S.V. Fomin and Ya. G. Sinai, Grundlehren der Mathematischen Wissenchaft 245, Springer.
  
  
• Ergodic problems of classical mechanics, by V.I. Arnold and A. Avez, Benjamin.
  
  
• Introduction to the modern theory of dynamical systems, by A. Katok, B. Hasselblatt, Cambridge University press.
  
  

Syllabus:

This course is an introduction to ergodic theory and dynamical systems. We will first introduce the basic concepts of ergodic theory: dynamical system, invariant measure, ergodicity and mixing. These will be illustrated with numerous examples (rotation of the circle, Bernouilli and Markov shifts, expanding maps, and so on) and their connection for example with probability, statistical mechanics and number theory. We then discuss the concept of entropy of a dynamical system and prove the variational principle as well as the Shannon Mc Millan theorem.

Homework:

Homework #1 PDF file      

Homework #2 PDF file      

Homework #3 PDF file