VO 25103.1 Ergodic Theory II

Lecturer: Prof. Henk Bruin

Email H. Bruin for further information for this course.

Announcements

Schedule

Contents of the 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.

Course Assessment

Will be based on an oral exam (in English by default, aber auf Deutsch ist auch möglich ).
For the oral exam, please make an appointment by email in due course.

References

• Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag 1975 ISBN 0-387-95152-0.
• Ricardo Mañé, Ergodic theory and differentiable dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete 8. Springer-Verlag, Berlin, 1987. ISBN: 3-540-15278-4
• Daniel Rudolph, Fundamentals of measurable dynamics, Oxford Science Publications, Clarendon Press Oxford 1990 ISBN 0-19-853572-4
• Karl Petersen, Ergodic Theory, Cambridge Studies in Advanced Mathematics, 1983, Cambridge University Press ISBN 0-521-38997-6
• Michael Brin and Garrett Stuck, Introduction to Dynamical Systems, Cambridge University Press 2002, ISBN 0-521-80841-3
• Omri Sarig, Lecture Notes on Ergodic Theory Penn State, Fall 2008, in .pdf

Course material (Hand-outs)

• Class notes in pdf. This set of notes may still be updated, and corrected.
• Class notes in pdf on thermodynamic formalism. This set of notes may still be updated, and corrected.