A dynamical approach to validated numerics

2022/03/28 by Oliver Jenkinson, Jenkinson, Oliver, Mark Pollicott +1 · 1 citation
Computer Science · Engineering · Mathematics · #11K55 #37D35 #37F35 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.15131

openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems. This leads to validated numerical estimates on their values

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• A pseudospectral approach to rigorous numerical estimation of Ruelle resonances of transfer operators

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