We use the Hénon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by measuring the time with a clock attached to the particle. We observe that the several events of time dilation that the particle undergoes exhibit sensitivity to the initial conditions. However, the structure of the singularities appearing in the escape time function remains invariant under coordinate transformations. This occurs because the singularities are closely related to the chaotic saddle. We then demonstrate using a Cantor-like set approach that the fractal dimension of the escape time function is relativistic invariant. In order to verify this result, we compute by means of the uncertainty dimension algorithm the fractal dimensions of the escape time functions as measured with an inertial frame and a frame comoving with the particle. We conclude that, from a mathematical point of view, chaotic transient phenomena are equally predictable in any reference frame and that transient chaos is coordinate invariant.

中文翻译：

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相对论系统中坐标转换下的暂时混乱。

我们使用Hénon-Heiles系统作为混沌散射的范式模型来研究洛伦兹因子对其瞬态混沌动力学的影响。特别是，我们关注通过在带有粒子的时钟的情况下测量时间来在散射区域内如何发生时间膨胀。我们观察到粒子经历时间膨胀的几个事件表现出对初始条件的敏感性。但是，在坐标变换下，出现在逸出时间函数中的奇异点的结构保持不变。发生这种情况是因为奇异点与混沌鞍座密切相关。然后，我们使用Cantor式集方法论证了逃逸时间函数的分形维数是相对论不变的。为了验证此结果，我们通过不确定性维数算法计算出逃逸时间函数的分形维数，该维数是用惯性框架和与粒子共同运动的框架测量的。我们得出的结论是，从数学角度来看，混沌瞬态现象在任何参考系中都是可预测的，并且瞬态混沌是坐标不变的。