New methods for analysing metastable structures in closed, open or non-autonomous dynamical systems (11frg168)


(Loughborough University)

Arno Berger (University of Alberta)

(University of Victoria)

Gary Froyland (UNSW Sydney)

(University of Victoria)

Rua Murray (University of Canterbury - New Zealand)


The "New methods for analysing metastable structures in closed, open or non-autonomous dynamical systems " workshop will be hosted at The Banff International Research Station.

Mathematical models play an increasing important role in research and development in diverse areas such as engineering, physics, the earth sciences, medical science, business and the social sciences. When the model represents time evolution of a physical system, the mathematical model is called a dynamical system. In addition to dynamical systems designed to study physical processes in other areas of science, there are dynamical systems arising naturally within mathematics itself. rnrnGiven a dynamical system, equilibrium structures are perhaps the first important feature to understand; they identify the long-term behavior(s) for the system. Next, the stability (or lack of stability) of equilibria play a critical role in the global behavior of a dynamical system. For systems out of equilibrium, the typical case, understanding the mechanism of transition to equilibrium is a natural feature to investigate. rnrnMore recently, attention has been focussed on non-equilibrium structures which none-the-less persist over long periods of time and play an important role in the structural evolution of the system. Various terms are used for these features: persistent structures, meta-stable states or quasi-invariant structures. The understanding of these objects for physically motivated dynamical systems is in its infancy, and the mathematical tools to analyze their behavior are just now being developed. Our proposal brings together researchers with diverse but related background suitable to study these questions. rnrnrn

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 US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí255a (CONACYT).