8 papers · 1 filter
Data-driven methods for computation of optimal linear response in high-dimensional dynamical systems
Gary Froyland, Dimitrios Giannakis, Nicholas Peters
We develop a data-driven framework for estimating optimal linear response of nonlinear dynamical systems. Our approach is based on kernel-smoothed approximations of the transfer/Ko…
Fixed-point approximation for self-consistent transfer operators with Newton's method
Wael Bahsoun, Gary Froyland, Maxence Phalempin
Self consistent transfer operators arise naturally in the study of mean-field coupled dynamical systems and are closely related to kinetic PDEs such as the Vlasov equation. Despite…
On the cardinality of measures of maximal relative entropy for smooth skew products
Matheus M. Castro, Gary Froyland
Let and be compact smooth manifolds and let be a skew-product diffeomorphism over a transitive Anosov base. We show that ha…
On the structure of complex spectra and eigenfunctions of transfer and Koopman operators
Matheus M Castro, Gary Froyland
Complex eigenspectra of transfer and Koopman operators describe rotational motion in dynamical systems. A particularly relevant situation in applications is when the rotation speed…
Learning dynamically inspired bases for Koopman and transfer operator approximation
Gary Froyland, Kevin Kühl
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the und…
Optimal linear response for Anosov diffeomorphisms
Gary Froyland, Maxence Phalempin
It is well known that an Anosov diffeomorphism enjoys linear response of its SRB measure with respect to infinitesimal perturbations . For a fixed observation function…
A tutorial on the dynamic Laplacian
Gary Froyland
Spectral techniques are popular and robust approaches to data analysis. A prominent example is the use of eigenvectors of a Laplacian, constructed from data affinities, to identify…
Identifying the onset and decay of quasi-stationary families of almost-invariant sets with an application to atmospheric blocking events
Aleksandar Badza, Gary Froyland
Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organises phase space. We intro…