有界和无界系统中李雅普诺夫指数的相对论不变性
Relativistic invariance of Lyapunov exponents in bounded and unbounded systems
摘要：
相对论系统中混沌的研究一直受到观测者依赖的李雅普诺夫指数（LE）和条件，如轨道有界性，调用在解释LE作为混沌的指标。在这里，我们建立了一个通用的框架，克服了这两个困难，并应用由此产生的方法来解决三个基本问题：如何LE变换下洛伦兹和Rindler变换和变换下均匀旋转的框架。对第一个和第三个问题的回答表明，惯性和均匀旋转的观察员同意的基础上LE的混沌的表征。另一方面，第二个问题是一个不适定的问题，由于事件视界固有的均匀加速的观察者。
英文摘要：
The study of chaos in relativistic systems has been hampered by the observer dependence of Lyapunov exponents (LEs) and of conditions, such as orbit boundedness, invoked in the interpretation of LEs as indicators of chaos. Here we establish a general framework that overcomes both difficulties and apply the resulting approach to address three fundamental questions: how LEs transform under Lorentz and Rindler transformations and under transformations to uniformly rotating frames. The answers to the first and third questions show that inertial and uniformly rotating observers agree on a characterization of chaos based on LEs. The second question, on the other hand, is an ill-posed problem due to the event horizons inherent to uniformly accelerated observers.
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