221 citations · 1.5k across the 51 of their papers we have counts for
56 papers
An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets
Jason Atnip, Gary Froyland, Péter Koltai
Lagrangian methods continue to stand at the forefront of the analysis of time-dependent dynamical systems. Most Lagrangian methods have criteria that must be fulfilled by trajector…
Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We study the quantitative simplicity of the Lyapunov spectrum of -dimensional bounded matrix cocycles subjected to additive random perturbations. In dimensions 2 and 3, we estab…
Optimal linear response for expanding circle maps
Gary Froyland, Stefano Galatolo
We consider the problem of optimal linear response for deterministic expanding maps of the circle. To each infinitesimal perturbation of a circle map we consider (i)…
A dynamic -Laplacian
Alvaro de Diego Unanue, Gary Froyland, Oliver Junge +1
We generalise the dynamic Laplacian introduced in (Froyland, 2015) to a dynamic -Laplacian, in analogy to the generalisation of the standard -Laplacian to the standard -La…
Revealing trends and persistent cycles of non-autonomous systems with operator-theoretic techniques: Applications to past and present climate dynamics
Gary Froyland, Dimitrios Giannakis, Edoardo Luna +1
An important problem in modern applied science is characterizing the behavior of systems with complex internal dynamics subjected to external forcings from their environment. While…
Compound Poisson statistics for dynamical systems via spectral perturbation
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We consider random transformations where each map acts on a complete metrizable space . The randomness comes from an…
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions
Gary Froyland, Christopher P. Rock
This paper investigates links between the eigenvalues and eigenfunctions of the Laplace-Beltrami operator, and the higher Cheeger constants of smooth Riemannian manifolds, possibly…
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems
Jason Atnip, Gary Froyland, Cecilia Gonzalez-Tokman +1
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to…
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean
Michael C Denes, Shane R Keating, Gary Froyland
The Southern Ocean plays an integral role in the global climate system, exchanging heat, salt, and carbon throughout the major ocean basins via the deep, fast-flowing Antarctic Cir…
Perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory
Jason Atnip, Gary Froyland, Cecilia Gonzalez-Tokman +1
We consider quasi-compact linear operator cocycles driven by an invertible ergodic pr…
Persistence and material coherence of a mesoscale ocean eddy
Michael C. Denes, Gary Froyland, Shane R. Keating
Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distan…
Deep Lagrangian connectivity in the global ocean inferred from Argo floats
Ryan Abernathey, Christopher Bladwell, Gary Froyland +1
We describe the application of a new technique from nonlinear dynamical systems to infer the Lagrangian connectivity of the deep global ocean. We approximate the dynamic Laplacian…
Equilibrium states for non-transitive random open and closed dynamical systems
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitiv…
Spectral analysis of climate dynamics with operator-theoretic approaches
Gary Froyland, Dimitrios Giannakis, Benjamin Lintner +2
The Earth's climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability…
Thermodynamic Formalism for Random Interval Maps with Holes
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to…
Detecting the birth and death of finite-time coherent sets
Gary Froyland, Péter Koltai
Finite-time coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some finite period of time; physical manifestations inc…
Optimal linear response for Markov Hilbert-Schmidt integral operators and stochastic dynamical systems
Fadi Antown, Gary Froyland, Stefano Galatolo
We consider optimal control problems for discrete-time random dynamical systems, finding unique perturbations that provoke maximal responses of statistical properties of the system…
Angular values of nonautonomous and random linear dynamical systems: Part I -- Fundamentals
Wolf-Jürgen Beyn, Gary Froyland, Thorsten Hüls
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimen…
Thermodynamic Formalism for Random Weighted Covering Systems
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random coveri…
Linear response for the dynamic Laplacian and finite-time coherent sets
Fadi Antown, Gary Froyland, Oliver Junge
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When…
Higher-Order Finite Element Approximation of the Dynamic Laplacian
Nathanael Schilling, Gary Froyland, Oliver Junge
The dynamic Laplace operator arises from extending problems of isoperimetry from fixed manifolds to manifolds evolved by general nonlinear dynamics. Eigenfunctions of this operator…
Fourier approximation of the statistical properties of Anosov maps on tori
Harry Crimmins, Gary Froyland
We study the stability of statistical properties of Anosov maps on tori by examining the stability of the spectrum of an analytically twisted Perron-Frobenius operator on the aniso…
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration
Gary Froyland, Péter Koltai, Martin Stahn
Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent…
A spectral approach for quenched limit theorems for random hyperbolic dynamical systems
D. Dragičević, G. Froyland, C. González-Tokman +1
We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving [DrFrGTVa18] to quenched random piecewise…