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

Author

Listed:
  • Amal Al Dowais

    (Department of Mathematics and Statistics, School of Physics, Mathematics and Computing, University of Western Australia, Perth, WA 6009, Australia
    Department of Mathematics, College of Science and Arts, Najran University, Najran 66262, Saudi Arabia)

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.

Suggested Citation

  • Amal Al Dowais, 2023. "Differentiability of the Largest Lyapunov Exponent for Non-Planar Open Billiards," Mathematics, MDPI, vol. 11(22), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4633-:d:1279271
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