Institut für Mathematik

Vorlesungen/Details

Ergodic theory

Dozent: Alexander Gorodnik

Vorlesungen

Di 10.15 - 12.00
Raum: Y27H12
Do 10.15 - 12.00
Raum: Y35F47

Übungen

Mo 10.15 - 12.00
n.n.
Exercises Ergodic theory

Description: The Ergodic Theory has its roots in the investigation of time-evolution and chaotic properties of complex physical systems. It was discovered that many such systems exhibit stable behavior on large time scales. The Ergodic Theory seeks for a rigorous explanation of this surprising phenomenon. In mathematical terms this involves analysis of groups of transformations of measure spaces that will be the main focus of the course. For instance, we will be interested in asymptotic behavior of iterations of these transformations, how to characterize randomness in this context, and how to compare/classify such systems. We will also discuss some of the applications of the Ergodic Theory to the other areas of mathematics.

Prerequisites: Analysis I-III

Assistant: Jialun Li

Lecture Notes: link

Exam: Februar 7, 2020

References:

  • Bekka and Mayer, Ergodic Theory and Topological dynamics of Group Actions on Homogeneous Spaces
  • Einsiedler and Ward, Ergodic Theory with a view towards Number Theory
  • Martin and England, Mathematical Theory of Entropy
  • Nadkarni, Basic ergodic theory
  • Walters, An Introduction to Ergodic Theory

Prüfung

Modul: 07.02.2020 9:00-12:00, Raum: n.n., Typ: schriftlich

Modul: MAT624 Ergodic theory