Ergodic Theory of Dynamical Systems (CM611)

CM611: Ergodic Theory of Dynamical Systems 

Prof. Constantin P. Niculescu


1. Dynamical systems with an invariant measure. Poincaré’s recurrence. The Bogoliubov-Krylov theorem.

2. The ergodic theorems of von Neumann and Birkhoff. Weyl’s ergodic theorem.

3. Mixing and ergodicity.

4. Metric entropy. Topological entropy. The variational principle.

5. Special classes of mappings. Piecewise monotonic mappings. Denjoy diffeomorphisms. Billiards.

6. Recurrence and its applications to combinatorics. The theorems of van der Waerden and Szemeredi.

7. The ergodic theorem of Oseledec. Liapunov Exponents. Applications to chaotic dynamical systems.




1. V.I. Arnold et A. Avez, Problèmes Ergodique de la Mecanique Classique. Gauthier-Villars, Paris, 1967.

2. Boyarsky A. and Góra P., Laws of Chaos. Invariant Measures and Dynamical Systems in One Dimension, Birkhäuser, 1997.

3. M. Gidea and C. Niculescu, Chaotic Dynamical Systems. An Introduction. Universitaria Press, Craiova, 2002.

4. R. Gologan, Applications of Ergodic Theory, Editura Tehnica, Bucharest, 1989 (Romanian)

5. R. Mañe, Ergodic Theory and Differentiable Dynamics, Springer-Verlag, 1987.

6. W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press, 1980.

7. Ya. G. Sinai, Topics in Ergodic Theory, Princeton Univ. Press, Princeton N.Y., 1994.

8. M. Viana, Dynamics: A Probabilistic and Geometric Perspective, Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998). Doc. Math. 1998, Extra Vol. I, 557-578 (electronic).

9. P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1982.

10. K. Yosida, Functional Analysis, 5th ed., Springer-Verlag, Berlin, 1995.

11. L.-S. Young, Ergodic theory of differentiable dynamical systems. In Real and Complex Dynamics, pp. 293-336, Ed. Branner and Hjorth, NATO ASI Series, Kluwer Academic Publ., 1995.