Differentiability of the Largest Lyapunov Exponent for Non-Planar Open Billiards

Amal Al Dowais ()
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Amal Al Dowais: Department of Mathematics and Statistics, School of Physics, Mathematics and Computing, University of Western Australia, Perth, WA 6009, Australia

Mathematics, 2023, vol. 11, issue 22, 1-21

Abstract: This paper investigates the behaviour of open billiard systems in high-dimensional spaces. Specifically, we estimate the largest Lyapunov exponent, which quantifies the rate of divergence between nearby trajectories in a dynamical system. This exponent is shown to be continuous and differentiable with respect to a small perturbation parameter. A theoretical analysis forms the basis of the investigation. Our findings contribute to the field of dynamical systems theory and have significant implications for the stability of open billiard systems, which are used to model physical phenomena. The results provide a deeper comprehension of the behaviour of open billiard systems in high-dimensional spaces and emphasise the importance of taking small perturbations into consideration when analysing these systems.

Keywords: open billiards; Lyapunov exponents; non-wandering set; billiard deformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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