250095 VO Ergodic Theorie/Ergodentheorie II

Lecturer: Prof. Henk Bruin

Email H. Bruin for further information for this course.


There will be no further lectures (i.e., with the Shannon-Breiman-McMillan Theorem covered in early January is the final topic of this course.

For the oral exam, please make an appointment by emailin due course.

The material is:


Day Time Room fromuntil
Wednesday 14:00-15:45 SR11 Lecture03.3.201423.06.2014
Wednesday 14:00-14:45 SR11 Lecture04.3.201425.06.2014

Contents of the course

This course goes deeper into ergodic theory, with main content: the theory of entropy and methods of thermodynamic formalism. Topics to be discussed are likely to include
- Definition and properties of entropy (both topological and metric). The variational principle.
- Entropy as invariant under isomorphism, and complete invariant under isomorphism for Bernoulli shifts.
- The Shannon-Breiman-McMillan Theorem.
- Basic notions and motivation of thermodynamic formalism.
- Applications of thermodynamic formalism to (fractal) dimension theory. Dimension formulas.
- Entropy and pressure for induced transformations (Abramov's formula).

The course will be given in English



Will be based on an oral exam (in English by default, aber auf Deutsch ist auch möglich ).

The material is:

Updated January 2015