Thermodynamic Formalism for Random Dynamical Systems

Jan de Gier

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

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.

This research program 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: 

Minicourses speakers:
Minicourse 1 – Mariusz Urbanski
Minicourse 2 – Carlangelo Liverani
Minicourse 3 – Hongkun Zhang

For talk titles and abstract, please click below

Participant List:
Jason Atnip (University of New South Wales)
Gary Froyland (University of New South Wales)
Cecilia González-Tokman (University of Queensland)
Sandro Vaienti (University of Toulon and Center of Theoretical Physics (Marseille))
Mariusz Urbański (University of North Texas)
Carlangelo Liverani (University of Rome Tor Vergata)
Hongkun Zhang (University of Massachusetts Amherst)
Yushi Nakano (Tokai University)
Wael Bahsoun (Loughborough University)
Rua Murray (University of Canterbury)
Charlene Kalle (Universiteit Leiden)
Matteo Tanzi (LPSM, CNRS-Sorbonne)
Meagan Carney (The University of Queensland)
Julia Slipantschuk (University of Warwick)
Renaud Daniel Jacques Leplaideur (IBS Center for Geometry and Physics)
Michael Horton (University of New South Wales)
Joshua Peters (The University of Queensland)
Andy Hammerlindl (Monash University)
Ayreena Bakhtawar (Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Pisa)
Renee Oldfield (The University of Queensland)
Caroline Wormell (Australian National University)

Registration is closed

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.