Dynamics on homogeneous spaces

Tel Aviv University, Fall 2013


Grading Here is the Exercise sheet. Exercises will be added from time to time. If you are taking the course for a grade, or if you just wanna have fun, solve as many as you can. If you are getting help from others or from books, give appropriate credit. Please submit your work by February 14, 2014 .




Notes In the lecture of 9.12.13 I didn't have time for some details of derivation of Theorem B from Theorem C. Here are notes with the missing Proposition: page 1, page 2, page 3, page 4.
In the lecture of 30.12.13 I didn't complete the proof of Theorem 2 or prove the wavefront lemma. Here are notes with the missing details: page 1, page 2, page 3, page 4.



Books

  • M. Einsiedler and T. Ward, Ergodic Theory: With a View Towards Number Theory
    (a general introduction to ergodic theory and dynamical systems).

  • B. Hasselblatt and A. Katok, Introduction to the Modern Theory of Dynamical Systems
    (another good general introduction although not as well suited for this course).

  • B. Bekka and M. Meyer, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces
    (a specialized monograph on the topics of the course, the pace is a little slower than ours).

  • M. Einsiedler and T. Ward, Homogeneous dynamics and applications
    (this is a draft of a book currently being written. E-mail me if you want a copy of this book which is currently being written. Comments appreciated by the authors.)

  • A. Starkov, Dynamical Systems on Homogeneous Spaces
    (an encyclopedic book that contains many of the results in the theory, more specialized than our course and contains more results in greater generality).