Open Dynamical Systems: Ergodic Theory, Probabilistic Methods and Applications (12w5050)


(Loughborough University)

(University of Victoria)

Gary Froyland (UNSW Sydney)


The Banff International Research Station will host the "Open Dynamical Systems: Ergodic Theory, Probabilistic Methods and Applications " workshop from April 8th to April 13th, 2012.

The research area known as dynamical systems studies mathematical models of phenomenon that evolve over time. Often, these are models of physical systems; examples of recent interest include ocean and atmospheric flows, trajectories of spacecraft, planetary motion, or models of biological or medical processes. A famous motivating example in the field is the study of billiards: the motion of one or more perfectly elastic balls on a flat table. In all of these examples the role of time evolution is clear. Much more subtle use of dynamics has led to important links with probability and stochastic processes, coding theory, aperiodic order (or quasicrystals) and mathematical number theory. In these areas, the notion of time evolution is not nearly so transparent.

Historically, dynamical systems are closed systems in the sense that trajectories are not allowed to leave the state space. Many powerful tools have been developed to compute the statistical behavior of orbits under this assumption. A natural and important extension is the concept of an "open system" where trajectories are occasionally allowed to leave the system and not return. The simplest analogy is a billiard table with a hole or pocket. A central question now takes the form: at what rate to the balls leave the table through the hole, and what is the statistical distribution of the balls remaining on the table at some specified time in the future?

The mathematical study of open dynamical systems is a new and important research area with a wide range of potential applications and many mathematical challenges. This conference aims to bring together both theoretical and applications-oriented researchers in order to link cutting-edge theoretical developments with new and interesting applications in mathematics, engineering and biology.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).