Long-time averaging for integrable Hamiltonian dynamics
Long-time averaging for integrable Hamiltonian dynamics
复制标题
可积哈密顿动力学的长时间平均
DOI：
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发表时间：
2005
影响因子：
2.1
通讯作者：
Gabriel Turinici
中科院分区：
文献类型：
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作者：
É. Cancès;F. Castella;P. Chartier;E. Faou;C. Bris;F. Legoll;Gabriel Turinici
摘要：给定一个哈密顿动力系统，我们讨论计算一个可观测量的时间平均极限的问题。对于一个完全可积的系统，遍历性可以由其频率上的丢番图条件来表征，并且这个极限与不变流形上的空间平均一致。在本文中，我们表明，我们可以提高收敛速度时，使用过滤功能的时间平均。然后，我们表明，这种收敛持续时，辛数值方案应用到系统中，积分器的顺序。
Summary.Given a Hamiltonian dynamical system, we address the question of computing the limit of the time-average of an observable. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that this limit coincides with the space-average over an invariant manifold. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a symplectic numerical scheme is applied to the system, up to the order of the integrator.