Thermodynamic Formalism for Random Dynamical Systems

Joy Lukman

  • 9 Jan 2023 - 20 Jan 2023
    8:00 am - 5:00 pm

Organisers:
Jason Atnip (University of New South Wales)
Gary Froyland (University of New South Wales)
Cecilia González-Tokman (University of Queensland)
Mariusz Urbański (University of North Texas)
Sandro Vaienti (Aix Marseille Université)

Program Description:
During the last 50 years, statistical properties of dynamical systems have been extensively studied. The resulting advances in statistical mechanics and thermodynamics, ergodic theory and probability theory, have had profound effects on mathematics, physics, engineering and biology. From the 1990s, using tools from probability theory, there have been major successes in understanding the rates of decay of statistical correlations and more general statistical properties of nonuniformly hyperbolic dynamical systems. These refined statistics allow better prediction of the behaviour of complex physical systems.

In a related direction, progress has been made on determining rates of convergence to limiting behaviour for a variety of quantities of physical relevance such as Lyapunov exponents, equilibrium measures, and ergodic sums amongst many others. These  developments have had application to homogenization theory, the modelling of weather and ocean systems, extreme value theory, and developing efficient numerical codes to model phenomena ranging from fluid flow to space missions. Recent years have seen important advances in the rigorous analysis of emergent stochastic behaviour of deterministic chaotic dynamical systems with often unexpected and practically relevant results.

The workshop will bring together experts in deterministic and random dynamics, as well as in applications, to allow transfer and exploitation of these ideas and set the research agenda for the coming years.

Program Structure: TBD

Registration:

  • Deadline: 9 November 2022
  • Registration is by invitation only.  If you are interested to participate in this research program, please contact one of the organisers with your CV and research background.

ASSOCIATED EVENTS

MATRIX Wine and Cheese Afternoon 10 January 2023
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.