Theory and Applications of the Mean Exponential Growth Factor of Nearby Orbits (MEGNO) Method
Theory and Applications of the Mean Exponential Growth Factor of Nearby Orbits (MEGNO) Method
复制标题
近轨平均指数增长因子(MEGNO)方法的理论与应用
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
C. Giordano
中科院分区：
文献类型：
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作者：
P. Cincotta;C. Giordano
在这一章中，我们讨论了教学的方式，从一开始的平均指数增长因子的邻近轨道（MEGNO）的方法，已被证明，在过去的十年中，是有效的调查定期和混沌的哈密顿系统的相空间的组成部分。它是一个快速的指标，提供了一个清晰的画面的共振结构，稳定和不稳定的周期轨道的位置，以及在混沌域的双曲性的措施，这与最大李雅普诺夫特征指数，但在较短的演化时间内给出的一致。简单的离散和连续动力系统的MEGNO的应用进行了讨论，并提供了一个概述的文献中包含相当不同的动力系统的稳定性研究。
In this chapter we discuss in a pedagogical way and from the very beginning the Mean Exponential Growth factor of Nearby Orbits (MEGNO) method, that has proven, in the last ten years, to be efficient to investigate both regular and chaotic components of phase space of a Hamiltonian system. It is a fast indicator that provides a clear picture of the resonance structure, the location of stable and unstable periodic orbits as well as a measure of hyperbolicity in chaotic domains which coincides with that given by the maximum Lyapunov characteristic exponent but in a shorter evolution time. Applications of the MEGNO to simple discrete and continuous dynamical systems are discussed and an overview of the stability studies present in the literature encompassing quite different dynamical systems is provided.