MAGIC010: Ergodic Theory

Course details

Semester

Spring 2010
Monday, January 11th to Friday, March 19th

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

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Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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