SoSe 17: Ergodentheorie und Transferoperatoren
Peter Koltai
Additional information / Pre-requisites
Literature:
- [Sa] Omri Sarig; Lecture Notes on Ergodic Theory (http://www.weizmann.ac.il/math/sarigo/sites/math.sarigo/files/uploads/ergodicnotes.pdf)
- [BG] Abraham Boyarsky, Pawel Góra; Laws of Chaos. Springer Science+Business Media New York, 1997
- [BS] Michael Brin and Garrett Stuck; Introduction to Dynamical Systems. Cambridge University Press, 2003
- [LM] Andrzej Lasota and Michael C. Mackey; Chaos, Fractals, and Noise. Springer, 1994
- [Wa] Peter Walters; An Introduction to Ergodic Theory. Springer, 1982
- [Ma] Ricardo Mañé; Ergodic Theory and Differentiable Dynamics. Springer, 1983
See also the related course from the summer term 2015: http://numerik.mi.fu-berlin.de/wiki/SS_2015/ErgodicTheory.php
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Ergodic theory in concerned with the behavior of dynamic systems when these are running for a long time. Vaguely speaking, the long-term statistical behavior of an ergodic dynamical system is not going to depend on its initial condition. This course discusses the mathematical characterization of this property. A central role is going to be played by the so-called transfer operator, which describes the action of the dynamics on a distribution of states. We are also going to highlight its importance in applications, when it comes to the numerical approximation of quantities of interest.
The course can be given in German or English.
close14 Class schedule
Regular appointments