# Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems

@article{GonzlezTokman2018MultiplicativeET, title={Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems}, author={Cecilia Gonz{\'a}lez-Tokman}, journal={Contemporary mathematics}, year={2018}, volume={709}, pages={31-52} }

We review state-of-the-art results on multiplicative ergodic theory for operators, with a view towards applications to the analysis of transport phenomena in non-autonomous dynamical systems, such as geophysical flows. The focus of this work is on ideas and motivation, rather than on proofs and technical aspects.

## 12 Citations

A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems

- MathematicsJournal of Computational Dynamics
- 2020

This work develops and implements algorithms providing multilayered descriptions of time-dependent systems which are not only useful for locating coherent structures, but also for detecting time windows within which these structures undergo fundamental structural changes, such as merging and splitting events.

Ju l 2 01 9 Computing covariant Lyapunov vectors in Hilbert spaces

- Mathematics
- 2019

Covariant Lyapunov vectors (CLVs) are intrinsic modes that describe long-term linear perturbations of solutions of dynamical systems. With recent advances in the context of semi-invertible…

A linear response for dynamical systems with additive noise

- MathematicsNonlinearity
- 2019

We show a linear response statement for fixed points of a family of Markov operators, which are perturbations of mixing and regularizing operators. We apply the statement to random dynamical systems…

Computing covariant Lyapunov vectors – A convergence analysis of Ginelli’s algorithm

- Mathematics
- 2020

Covariant Lyapunov vectors (CLVs) are intrinsic modes that describe long-term linear perturbations of solutions of dynamical systems. Similar to eigenmode decompositions for steady states, they form…

Computing Covariant Lyapunov Vectors in Hilbert spaces

- MathematicsJournal of Computational Dynamics
- 2021

<p style='text-indent:20px;'>Covariant Lyapunov Vectors (CLVs) are intrinsic modes that describe long-term linear perturbations of solutions of dynamical systems. With recent advances in the context…

On the Computation of the Extremal Index for Time Series

- MathematicsJournal of Statistical Physics
- 2019

The extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances. In the dynamical systems framework, it provides important information about the…

Historic behaviour for nonautonomous contraction mappings

- MathematicsNonlinearity
- 2019

We consider a parametrised perturbation of a diffeomorphism on a closed smooth Riemannian manifold with , modeled by nonautonomous dynamical systems. A point without time averages for a…

From metastable to coherent sets- Time-discretization schemes.

- Computer Science, MathematicsChaos
- 2019

It is shown that well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems, and their applicability in two different fields of application is shown.

Random historic behaviour

- Mathematics
- 2017

The point with no time averages for a random dynamical system $f$ is said to have historic behaviour. It is known that for any absolutely continuous random dynamical system of $\mathscr C^r$…

Stability of hyperbolic Oseledets splittings for quasi-compact operator cocycles

- Computer ScienceDiscrete & Continuous Dynamical Systems
- 2022

A random version of the perturbation theory of Gouëzel, Keller, and Liverani is developed, which provides a unifying framework for key concepts in the so-called 'functional analytic' approach to studying dynamical systems, and has applications to the construction of anisotropic norms adapted to dynamical Systems.

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