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:

- Definition and properties of entropy (both topological and metric).
- Basic examples of computation of entropy (Bernoulli shifts, piecewise linear interval maps.
- The variational principle.
- Basic notions and motivation of thermodynamic formalism.
- Applications of thermodynamic formalism to (fractal) dimension theory. (including dimension formulas).
- The Shannon-Breiman-McMillan Theorem.

Day | Time | Room | from | until | |
---|---|---|---|---|---|

Wednesday | 14:00-15:45 | SR11 | Lecture | 03.3.2014 | 23.06.2014 |

Wednesday | 14:00-14:45 | SR11 | Lecture | 04.3.2014 | 25.06.2014 |

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).

- Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag 1975 ISBN 0-387-95152-0.
- Gerhard Keller, Equilibrium States in Ergodic Theory, Cambridge Univ. Press. 1998
- Rufus Bowen, Equilibrium states and ergodic Theory of Anosov Diffeomorphisms, Springer-Verlag, Lect. Notes in Mathematics, 470, 1975.
- Omri Sarig, Lecture Notes on Thermodynamic Formalism for Topological Markov Shifts. Penn State, 2009.
- Omri Sarig, Lecture Notes on Ergodic Theory Penn State, Fall 2008, in .pdf and the later version: in .pdf
- Class notes of Ergodic Theory I (SS2014) pdf, updated November 4 2014. This set of notes may still be updated, and corrected.
- Class notes of Thermodynamic Formalism I (WS2012) pdf.

Class Notes from earlier courses:

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

The material is:

- Definition and properties of entropy (both topological and metric).
- Basic examples of computation of entropy (Bernoulli shifts, piecewise linear interval maps.
- The variational principle.
- Basic notions and motivation of thermodynamic formalism.
- Applications of thermodynamic formalism to (fractal) dimension theory. (including dimension formulas).
- The Shannon-Breiman-McMillan Theorem.

Updated January 2015