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General


Semester

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

Timetable
  • Wed 12:05 - 12:55

Lecturer


Charles Walkden
Email charles.walkden@manchester.ac.uk
Phone (0161) 2755805
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Students


Photo of Andrew Barwell
Andrew Barwell
(Birmingham)
Photo of Alistair Bird
Alistair Bird
(Lancaster)
Photo of Femke Douma
Femke Douma
(Durham)
Photo of Charles Eaton
Charles Eaton
(Manchester)
Photo of Ben Fairbairn
Ben Fairbairn
(Birmingham)
Photo of Andrew Hayden
Andrew Hayden
(Durham)
Photo of James Hook
James Hook
(Manchester)
Photo of Mark Kambites
Mark Kambites
(Manchester)
Photo of Tri N. Ta
Tri N. Ta
(Lancaster)
Photo of Silvia Pina-Romero
Silvia Pina-Romero
(Manchester)
Photo of Adam Skalski
Adam Skalski
(Lancaster)
Photo of Rob Sturman
Rob Sturman
(Leeds)
Photo of Francesca Ticconi
Francesca Ticconi
(Sheffield)


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.

Bibliography


No bibliography has been specified for this course.

Assessment


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