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Description: Ergodic theory is 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 higlight its importance in applications, when it comes to the numerical approximation of quantities of interest. If time permits, we will introduce entropy, as a notion of complicatedness (or "non-predictability") of a dynamical system. Planned content
Zielgruppe: Masterstudenten, oder Fortgeschrittene Bachelorstudenten Voraussetzungen: Maßtheorie und grundlegende Kenntnisse aus der Funktionalanalysis. Von Vorteil, aber nicht notwendig: grundlegende Kenntnisse aus der Theorie dynamischer Systeme (z.B. die Vorlesung Differentialgleichungen I)
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