The year 2015 marks the 50-year anniversary of Oseledets’ groundbreaking multiplicative ergodic theorem (MET). As discussed in the Overview section, METs provide a framework for the study of RDS in a way that, at an abstract level, one can attempt to export techniques originally developed for autonomous systems to the setting of RDS.

A good number of the expected participants are experts in RDS, several more have made substantial contributions to the theory of METs or stochastic PDEs in the last decade, and a third group has successfully applied the theory of RDS in the context of real-world problems. The research of each of these groups is currently undergoing vigorous developments, and Banff will be the ideal environment to foster meaningful research interactions among these communities.

The concrete objectives of the workshop are:

(i) To provide an overview of the latest advances in theoretical, applied and numerical sides of the subject.

(ii) To extend the scope of autonomous dynamical systems techniques and ideas to the random setting. This includes qualitative as well as quantitative features of interest.

(iii) To explore the applicability of multiplicative ergodic theorems to random dynamical systems, including stochastic PDEs.

(iv) To advance the understanding of the relation between components of Oseledets splittings and dynamically relevant phenomena, such as metastability and coherence.

(v) To expand the set of RDS tools employed in the study of real-world models. These tools should include the latest theoretical advances.

(vi) To identify and research concrete major applied questions that would benefit from new theoretical and numerical developments in the theory of RDS.