Dynamics and Statistics of Spatially Extended Systems (09w5085)

Arriving in Banff, Alberta Sunday, January 18 and departing Friday January 23, 2009


Konstantin Khanin (University of Toronto)

(Georgia Institute of Technology)


The workshop will include talks on probabilistic approaches in both finite-dimensional and
spatially extended cases. Below we list some of the problems for infinitely-dimensional
systems which we plan to address.

1. Invariant measures for stochastic PDE's (Navier-Stokes, Burgers and others).

2. Blow-up phenomenon and renormalization.

3. Space-time chaos and phase transitions for coupled map lattices.

4. Network Synchronization (with applications in neurobiology).

5. Averaging theory for spatially-extended system.

6. Fourier law and heat transport.

To the best of our knowledge this is the first workshop with a focus on mathematical
problems in the theory of
infinite-dimensional dynamical systems which brings together mathematicians, theoretical
physicists and researches working on practical applications.
A number of leading experts including
V. Afraimovich, D. Campbell, N. Chernov, D. Dolgopyat,
V. Kaloshin, J. Lebowitz, C. Liverani, A. Neishtadt, Y. Pesin,
V. Rom-Kedar, M. Rabinovich, S. Shlosman, A. Shirelman,
M. Shub, Ya. Sinai, D. Szasz, L-S Young, G Zaslavski
expressed their strong interest in participating. We are confident that we will
be able to attract a very strong group of researchers, including experts in applications.

In our opinion the expertise accumulated recently in the theory of dynamical system
gives a real hope for a very significant improvement of our understanding
of spatially extended systems. Such an improvement is the main goal of the proposed