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Spring 2008 (Monday, January 21 to Friday, March 14; Monday, April 28 to Friday, May 16)


  • Wed 12:05 - 12:55


No prerequisites information is available yet.


  • 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.


Charles Walkden
Phone (0161) 2755805


Photo of Andrew Barwell
Andrew Barwell
Photo of Alistair Bird
Alistair Bird
Photo of Femke Douma
Femke Douma
Photo of Charles Eaton
Charles Eaton
Photo of Ben Fairbairn
Ben Fairbairn
Photo of Andrew Hayden
Andrew Hayden
Photo of James Hook
James Hook
Photo of Mark Kambites
Mark Kambites
Photo of Tri N. Ta
Tri N. Ta
Photo of Silvia Pina-Romero
Silvia Pina-Romero
Photo of Adam Skalski
Adam Skalski
Photo of Rob Sturman
Rob Sturman
Photo of Francesca Ticconi
Francesca Ticconi


No bibliography has been specified for this course.


No assessment information is available yet.

No assignments have been set for this course.

Recorded Lectures

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