2019/07/25 by Fadi Antown, Gary Froyland, Antown, Fadi +3
Mathematics · Physics and Astronomy · #35J15 #37C05 #37C10 #37C30 #37M99 #47A55 #Applied mathematics #Computer science #Dynamical Systems (math.DS) #Eigenfunction #Eigenvalues and eigenvectors #FOS: Mathematics #Finite element method #Laplace operator #Laplace transform #Mathematical analysis #Mathematics #Mixing (physics) #Nonlinear system #Operator (biology) #Physics #Quantum chaos and dynamical systems #math.DS #msc:35J15 #msc:37C05 #msc:37C10 #msc:37C30 #msc:37M99 #msc:47A55
paper · pdf · doi:10.48550/arxiv.1907.10852
openalex publication_date 2019/07/25 · arxiv created 2021/04/13 · arxiv updated 2021/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.