By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV exponent together affect the chaotic dynamics of this system. The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value z ∗ = 2, below which the string is captured by the black brane no matter where the string is placed at the beginning. However, when z > 2, the string escapes to infinity if it is placed near the black brane at the beginning, but if the initial position of string is far away from the black brane, it oscillates around the black brane till eternity, which is a quasi-periodic motion. HV exponent plays the role of driving the string falling into the black brane. With the increase of HV exponent θ , the falling velocity becomes faster. We find that when we heat the system with large HV exponent, the chaotic system does not essentially changes. It indicates that the HV exponent plays a very important role in determining the state of the chaotic system. Also we study the effect from the winding number of the string. The study indicates that the chaotic dynamics of the string is insensitive to the winding number.

中文翻译：

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带超标度违规的带电黑膜周围串的混沌动力学

通过快速李雅普诺夫指标 (FLI)，我们研究了具有超标度违规 (HV) 的带电黑膜周围闭合弦的混沌动力学。霍金温度、Lifshitz 动力学指数和 HV 指数共同影响该系统的混沌动力学。温度起着驱使闭合弦向无穷大逃逸的作用。有一个阈值 z ∗ = 2，低于该阈值的字符串被黑膜捕获，无论字符串放在开头的什么位置。但是，当 z > 2 时，如果开始时放在靠近黑膜的位置，弦会逃逸到无穷远，但如果弦的初始位置远离黑膜，则它会绕着黑膜振荡直到永恒，即准周期运动。HV指数起到驱使弦落入黑膜的作用。随着 HV 指数 θ 的增加，下落速度变快。我们发现，当我们加热具有大 HV 指数的系统时，混沌系统并没有本质上的变化。这表明 HV 指数在决定混沌系统的状态方面起着非常重要的作用。我们还研究了弦数的影响。研究表明，弦的混沌动力学对缠绕数不敏感。