MS34 Transfer Operator Methods for Open and Nonautonomous Systems with Applications

Nonlinear dynamical systems often exhibit essentially random temporal behavior. It then makes more sense to analyse the statistical long term properties of solution ensembles, rather than individual solutions. A powerful tool in this analysis is the transfer operator, which represents the pushforward of densities (wrt some standard volume), as the spectral properties of the transfer operator directly relate to statistical properties of the dynamics. This approach was first developed for autonomous systems on compact state spaces.

In this minisymposium, we will consider open systems (where trajectories may escape), as well as random systems (resulting in a random transfer operators). Studying the transfer operators again allows conclusions on the long term statistical properties of the dynamics. For open systems for instance one finds conditionally invariant probabilities while random transfer operators can be used to study pullback invariant measures.

S. Vaienti will give an overview over transfer operator methods in open systems, while P. Giulietti will talk about statistical extremes for open systems. The work by L. Oljaca uses (Hilbert) projective metrics on cones to analyse random transfer operators which arise in nonlinear filtering (motivated by Data Assimilation techniques in Weather, Climate, and Oceans). K. Padberg-Gehle will present an application to coherent structures in fluid flows.

Organizer: Jochen Broecker, University of Reading, United Kingdom
Tobias Kuna, University of Reading, United Kingdom

12:15-12:40 Thermodynamic Formalism for Random Covering Systems abstract

Sandro Vaienti, Aix-Marseille University and Universite de Toulon, France; Jason Atnip and Gary Froyland, University of New South Wales, Australia; Cecilia Gonzalez-Tokman, University of Queensland, Australia

12:45-1:10 Extreme Value Theory via Transfer Operators abstract

Paolo Giulietti, Università di Pisa, Italy

1:15-1:40 Stability of the Nonlinear Filter for Anosov Diffeomorphisms abstract

Lea Oljaca, University of Exeter, United Kingdom; Jochen Broecker and Tobias Kuna, University of Reading, United Kingdom

1:45-2:10 Applications of Transfer Operator Methods in Fluid Dynamics abstract

Kathrin Padberg-Gehle, Leuphana University Lueneburg, Germany

For more information please visit the event page.

This minsymposium is part of the SIAM Conference on Applications of Dynamical Systems (DS21), May 23 – 27, 2021, Virtual Conference.