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Graduate (MAGIC) Course on Ergodic Theory

Prize winner, Teaching DS Competition, 2013

By Charles Walkden
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Graduate (MAGIC) Course on Ergodic Theory
These notes form a 10-lecture course on ergodic theory and its applications to hyperbolic dynamical systems. The level of material is suitable for beginning graduate students in mathematics who want to either gain an overview of various aspects of ergodic theory, or want to gain a more detailed understanding of the ergodic theory of hyperbolic dynamical systems via thermodynamic formalism. 

Topics covered include: examples of dynamical systems, uniform distribution mod 1, invariant and ergodic measures, ergodic theorems and recur- rence, measure-theoretic and topological entropy, thermodynamic formalism, the ergodic theory of hyperbolic dynamical systems.

The course consists of 10 lectures. Each lecture has a set of slides (slides link) and an accompanying set of more detailed lecture notes (notes link). The slides were developed to be used in a MAGIC course (see below), but can also be used for self-study for those who only want/need an overview of the subject. The lecture notes provide details (proofs, additional commentary, etc) for those who are interested in the technical details, and are intended to be used as self-study material. The lecture notes also contain exercises.

MAGIC (=Mathematics Access Grid: Instruction and Collaboration) is a network of 19 mathematics departments at universities in the UK and provides graduate level courses to first year PhD students in pure and applied mathematics. The courses are intended to widen students’ knowledge of mathematics, rather than provide training in their research area. The lectures are given via Access Grid video-conferencing technology. I have given a course on ergodic theory using these notes as part of MAGIC every year since its inception in 2008.
Author Institutional Affiliation
Charles Walkden
School of Mathematics
The University of Manchester
Author Email
Tutorial LevelAdvanced Tutorial
DescriptionNotes
Contest EntryYes

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