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Elijah Ward
Elijah Ward

Walters Introduction To Ergodic Theory Pdf Download

In the broadest sense, ergodic theory is the study of group actions on measure spaces. Its history traces from Poincare's recurrence theorem in celestial mechanics and Boltzman's ergodic hypothesis in statistical physics to its mathematical proliferation in the 1930s through the ergodic theorems of von Neumann, Birkhoff, and Koopman. It has since grown into a hugely important research area with striking applications to other areas of mathematics. This course provides an introduction to the basics of ergodic theory. Among other things, this includes the theory of recurrence, the structure and convergence of ergodic averages, and the notion of entropy. We will motivate the main ideas and results through simple examples. Another focal point lies on the many groundbreaking applications of ergodic theory in number theory.

walters introduction to ergodic theory pdf download


This course is aimed at master's or advanced bachelor's students. Since ergodic theory is largely based on the notions of measure theory, either some background in measure theory or the willingness to learn some of this material along the way is expected. I will provide a handout summarizing the prerequisites from measure theory that are needed for this course at the beginning of the semester.

  • Formalize dynamcial ideas and concepts such as ergodicity, entropy, chaos, determinism, etc.

  • Apply tools and techniques from ergodic theory in number theory and combinatorics

  • Interpret examples of dynamical systems

  • Prove results in ergodic theory


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