for this workshop
Stochastic methods for non-equilibrium dynamical systems
American Institute of Mathematics, San Jose, California
Mark Demers, Renato Feres, Matthew Nicol, and Hongkun Zhang
This workshop, sponsored by AIM and the NSF, will be devoted to the study of the statistical properties of dynamical systems of physical interest. Such systems include mathematical billiards and their perturbations, more general Hamiltonian mechanical systems on manifolds with boundary, the Lorentz flow, intermittent maps which model systems with slowly mixing or ''sticky'' regions, and random dynamical systems from non-equilibrium statistical physics. In particular, this workshop will seek to exploit recent advances in techniques to study non-uniformly hyperbolic systems in order to expand our understanding of statistical properties such as decay of correlations, large deviations, return time statistics and related limit laws. The workshop will bring together experts in spectral techniques, coupling, statistical mechanics and probabilistic dynamics.
The main topics for the workshop are:
- Investigate properties of dynamical systems of physical interest, including systems out of equilibrium. This focus includes billiards and their perturbations, including systems under external forces and time dependent systems that lack a stationary distribution. A main thrust for this class of systems is to develop a rigorous theory for such issues as entropy production, transport and diffusion coefficients.
- Develop a broader understanding of advanced statistical properties, such as extreme value theory, return time statistics, and large deviations theory for a broad class of dynamical systems of physical interest. In particular, some recently constructed slowly mixing billiards systems are expected to obey stable limit laws.
- Explore new model systems of interest to applied scientists and engineers, such as Knudsen diffusion in nano-structured channels and thermo-mechanical behavior of nano devices. The interaction of theoretical and applied mathematicians will be enhanced by the physical relevance of the systems under consideration and is a crucial aspect of the workshop.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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