This course is an introduction to ergodic theory, which studies group actions on measure spaces and is largely concerned with the asymptotic and perturbative behavior of such dynamical systems. The subject traces its roots back to classical and statistical mechanics and has a wide range of applications throughout mathematics, from number theory and operator algebras to differentiable dynamics and the rigidity theory of Lie groups and their lattices. The topics covered in the course include the ergodic theorems of von Neumann and Birkhoff, the Rokhlin lemma, mixing properties, amenability, and entropy. Basic knowledge of point-set topology and measure and integration theory will be assumed. The course can be taken as the first part of a functional analysis Vertiefungsmodul in the Bachelor's program, or as part of a Verbreiterungsmodul in the Master's program.

Resources:

• Ergodic Theory with a View Towards Number Theory, by Manfred Einsielder and Thomas Ward. Springer, London, 2011.
• Ergodic Theory, by Karl Petersen. Cambridge University Press, Cambridge, 1989.
• An Introduction to Ergodic Theory, by Peter Walters. Springer, New York, 2000.
• Ergodic Theory – Introductory Lectures, by Peter Walters. Springer, Berlin, 1975.
• Ergodic Theory: Independence and Dichotomies, by David Kerr and Hanfeng Li. Springer, Cham, 2016.

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