Time-frequency analysis of chaotic systems

被引：128
作者：
Chandre, C
Wiggins, S
Uzer, T
机构：
[1] CNRS, Ctr Phys Theor, F-13288 Marseille 09, France
[2] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
[3] Georgia Inst Technol, Sch Phys, Ctr Nonlinear Sci, Atlanta, GA 30332 USA
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2003年 / 181卷 / 3-4期
基金：
美国国家科学基金会;
关键词：
time-frequency analysis; wavelets; Hamiltonian systems;
D O I：
10.1016/S0167-2789(03)00117-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also called instantaneous frequencies, enable us to analyze the phase space structures. In particular, this method detects resonance trappings and transitions and allows a characterization of the notion of weak and strong chaos. We illustrate the method with the trajectories of the standard map and the hydrogen atom in crossed magnetic and elliptically polarized microwave fields. (C) 2003 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：171 / 196
页数：26
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