Stochastic methods for non-equilibrium dynamical systems
June 1 to June 5, 2015
American Institute of Mathematics,
San Jose, California
and Hongkun Zhang
This workshop 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
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
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.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Papers arising from the workshop:
A spectral approach for quenched limit theorems for random expanding dynamical systems
by Davor Dragicevic, Gary Froyland, Cecilia Gonzalez-Tokman, and Sandro Vaienti, Comm. Math. Phys. 360 (2018), no. 3, 1121–1187 MR3803820
Stochastic dynamics: Markov chains and random transformations
by Felix X.-F. Ye, Yue Wang and Hong Qian, Discrete Contin. Dyn. Syst. Ser. B 21 (2016), no. 7, 2337–2361 MR3543636
Almost sure invariance principle for random piecewise expanding maps
by D. Dragicevic, G. Froyland, C. González-Tokman and S. Vaienti