MAGIC010: Ergodic Theory

Course details

A specialist MAGIC course

Semester

Spring 2009
Monday, January 19th to Friday, March 27th; Monday, April 27th to Monday, April 27th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Wednesdays
12:05 - 12:55

Description

Prerequisites

No prerequisites information is available yet.

Syllabus

  • Lecture 1: Examples of dynamical systems (maps on a circle, the doubling map, shifts of finite type, toral automorphisms, the geodesic flow)
  • Lecture 2: Uniform distribution, inc. applications to number theory
  • Lecture 3: Invariant measures and measure-preserving transformations. Ergodicity.
  • Lecture 4: Recurrence and ergodic theorems (Poincaré recurrence, Kac's lemma, von Neumann's ergodic theorem, Birkhoff's ergodic theorem)
  • Lecture 5: Applications of the ergodic theorem (normality of numbers, the Hopf argument, etc)
  • Lecture 6: Mixing. Spectral properties.
  • Lecture 7: Entropy and the isomorphism problem.
  • Lecture 8: Topological pressure and the variational principle.
  • Lecture 9: Thermodynamic formalism and transfer operators.
  • Lecture 10: Applications of thermodynamic formalism: (i) Bowen's formula for Hausdorff dimension, (ii) central limit theorems.

Lecturer

  • CW

    Dr Charles Walkden

    University
    University of Manchester

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

Only consortium members have access to these files.

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.