2025/04/23 by Gary Froyland, Froyland, Gary, Maxence Phalempin +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2504.16532
openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
It is well known that an Anosov diffeomorphism T enjoys linear response of its SRB measure with respect to infinitesimal perturbations T. For a fixed observation function c, we develop a theory to optimise the response of the SRB-expectation of c. Our approach is based on the response of the transfer operator on the anisotropic Banach spaces of Gouëzel--Liverani. We prove that the optimising perturbation T is unique for non-degenerate response functions and provide explicit expressions for the Fourier coefficients of T. We develop an efficient Fourier-based numerical scheme to approximate the optimal vector field T, along with a proof of convergence. The utility of our approach is illustrated in two numerical examples, by localising SRB measures with small, optimally selected, perturbations.