A dynamical approach to validated numerics
Oliver Jenkinson, Mark Pollicott
TL;DR
This paper introduces a dynamical method utilizing periodic points and determinants to compute and validate key dynamical quantities like Lyapunov exponents and Hausdorff dimensions in hyperbolic systems, enabling reliable numerical estimates.
Contribution
It presents a novel approach that provides alternative expressions and validated numerical estimates for dynamical invariants in hyperbolic systems.
Findings
Validated numerical estimates for Lyapunov exponents
Validated estimates for Hausdorff dimension
New expressions for dynamical quantities
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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Taxonomy
TopicsMathematical Dynamics and Fractals · Stability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering