WiSe 20/21: Ergodic theory and transfer operators
Péter 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 on the long run, and provides statistical statements thereof. It delivers a statistical forecast for system, which are otherwise unpredictlable (e.g., chaotic or genuinely stochastic).
This course discusses the mathematical characterization of this situation. 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 and data-driven approximation of quantities of interest.
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Suggested reading
- [Sa] Omri Sarig; Lecture Notes on Ergodic Theory
- [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
15 Class schedule
Regular appointments