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Oseledets splittings for semi-invertible linear cocycles: Existence, stability, and applications

Banff International Research Station for Mathematical Innovation and Discovery

I will report on a program of work to establish existence and stability results for linear cocy- cles in the semi-invertible situation - where the driving mechanism is invertible, but the linear actions may be non-injective - and to create numerical methods to apply to real-world models and data. The “existence of Oseledets splitting” results provide a stronger multiplicative ergodic theorem than the “classical” theorems, which only guarantee the existence of measurable Os- eledets filtrations. The stability results concern continuity properties of the Lyapunov exponents and their corresponding splitting elements when the linear actions are subjected to a variety of perturbations. The applied motivations for this work are the detection and tracking of so-called coherent structures in time-dependent dynamical systems, and I will also report on the applica- tion of these constructions to fluid flow in the ocean and atmosphere. This is joint work with Cecilia Gonz ́alez Tokman, Christian Horenkamp, Simon Lloyd, Adam Monahan, Anthony Quas, Vincent Rossi, Naratip Santitissadeekorn, Alex Sen Gupta, and Erik van Sebille.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Dynamical systems

video/mp4

Author affiliation: University of New South Wales

2015-07-22

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/54129

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/