UK Nonlinear News, November 2001

Probabilistic methods in non-hyperbolic dynamics

University of Surrey: 28th August - 1st September 2001

By Ian Melbourne and Matthew J. Nicol

An ESF PRODYN (``Probabilistic methods in non-hyperbolic dynamics'') Workshop on the Statistical Properties of Dynamical Systems, (with a particular emphasis on compact group extensions) was held at the University of Surrey from Tuesday, 28 August to Saturday, 1 September 2001. The local organisers were Ian Melbourne and Matthew Nicol and participants included O. Bandtlow, J. P. Conze, M. Field, M. Holland, O. Jenkinson, F. Ledrappier, M. Pollicott, M. Rams, O. Sarig, R. Sharp, A. Torok and C. Walkden.

Topics and projects discussed included

  1. methods of establishing rates of decay of correlations and central limit theorems for partially hyperbolic systems.
  2. invariance principles for certain classes of observations on compact group extensions of Axiom A flows and extending such results to the setting of compact group extensions of nonuniformly hyperbolic diffeomorphisms and flows.
  3. stable transitivity of partially hyperbolic systems
  4. geometric rigidity theorems.

The meeting was very successful in that several new results were announced and new directions of research were suggested. It also was a focused meeting since talks and mathematical discussions were directly related to the theme of the meeting.

We would like to thank the ESF - ``Probabilistic methods in non-hyperbolic dynamics'' (PRODYN) Programme for sponsoring our meeting.

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