Linear response for the dynamic Laplacian and finite-time coherent sets. (12th May 2021)

• Record Type: Journal Article
• Authors: Antown, Fadi; Froyland, Gary; Junge, Oliver
• Is Part Of: Nonlinearity. Volume 34:Number 5(2021)
• Page Start: 3337
• Page End: 3355
• Publication Date: 2021-05-12
• Subjects: linear response -- coherent set -- dynamic Laplacian; 37C05 -- 37C10 -- 37C30 -- 37M99 -- 35J15 -- 47A55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abe834
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: 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 the dynamical system is subjected to small parameter change, one can ask about the rate of change of (i) the location and shape of the coherent sets, and (ii) the mixing properties (how much more or less mixing), with respect to the parameter. We answer these questions by developing linear response theory for the eigenfunctions of the dynamic Laplace operator, from which one readily obtains the linear response of the corresponding coherent sets. We construct efficient numerical methods based on a recent finite-element approach and provide numerical examples.