An Introduction to the Ergodic Theory
From Wednesday, 15. September 2004
To Monday, 30. May 2005
Hits : 33
Teacher:
Lluís Alsedà (UAB)

Program:
  1. Preliminary measure theory
  2. Ivariant measures and basic ergodic theory: Invariant measures. Theorem of Krylov-Bogolubov. Poincaré recurrence. Ergodic measures. Ergodic decomposition. Birkhoff ergodic theorem. Ergodicity and mixing. Factors and extensions.
  3. Ergodic theory for manifolds and Liapunov exponents: The subaditive ergodic theorem. Oseledec-type theorems. Liapunov Exponents. Examples. The Smale's Horseshoe.
  4. Entropy: Information and entropy of partitions. Entropy of dynamical systems. Kolmogorov-Sinai Theorem. Entropy as a function of the measure. Metric and topological entropy and the variational principle. Relationship between the entropy and the Liapunov exponents.
Location Universitat Autònoma de Barcelona