标题： 非平面开放散射系统的最大李雅普诺夫指数的可微性 显示英文标题

标题： Differentiability of the largest Lyapunov exponent for non-planar open billiards

摘要： 本文研究了高维空间中开放弹道系统的特性。 具体而言，我们估计了最大的李雅普诺夫指数，该指数量化了动力系统中相邻轨迹的发散速率。 该指数被证明相对于一个小扰动参数是连续依赖且可微的。 理论分析是本研究的基础。 我们的研究结果对动力系统理论领域做出了贡献，并对用于模拟物理现象的开放弹道系统的稳定性具有重要意义。 结果提供了对高维空间中开放弹道系统行为的更深入理解，并强调了在分析这些系统时考虑小扰动的重要性。 显示英文摘要

摘要： 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 continuously dependent 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.