Titlebook: Operator Theoretic Aspects of Ergodic Theory; Tanja Eisner,Bálint Farkas,Rainer Nagel Textbook 2015 Tanja Eisner, B�lint Farkas, Markus Ha

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Measure-Preserving Systems,In the previous chapters we looked at topological dynamical systems, but now let us turn to dynamical systems that preserve some probability measure on the state space. We shall first motivate this change of perspective.

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The Pointwise Ergodic Theorem,While von Neumann’s mean ergodic theorem is powerful and far reaching, it does not actually solve the original problem of establishing that “time mean equals space mean” for a given measure-preserving system ..

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Topological Dynamics and Colorings,In this chapter we explain the connection between coloring results from combinatorics and topological dynamical systems, an aspect that was discovered by Furstenberg and Weiss. Since their seminal paper (Furstenberg and Weiss 1978b) a new area has emerged that has been an active field of research ever since.

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atikern in den letzten hundert Jahren nicht die gleiche Pflege erhalten wie die anderen Zweige. Früher, als noch Personalunion in den Reichen der Mathematik, der Astronomie, der Physik bestand, war das anders. . z. B. hat den Methoden des numerischen Rechnens, der Interpolation, der Integration, der

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