Time-frequency analysis of chaotic systems

C Chandre; SR Wiggins; T Uzer

doi:10.1016/S0167-2789(03)00117-9

Time-frequency analysis of chaotic systems

C Chandre, SR Wiggins, T Uzer

Research output: Contribution to journal › Article (Academic Journal) › peer-review

125 Citations (Scopus)

Abstract

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.

Translated title of the contribution	Time-frequency analysis of chaotic systems
Original language	English
Pages (from-to)	171 - 196
Number of pages	26
Journal	Physica D: Nonlinear Phenomena
Volume	181 (3-4)
DOIs	https://doi.org/10.1016/S0167-2789(03)00117-9
Publication status	Published - Jul 2003

Bibliographical note

Publisher: Elsevier Science BV
Other identifier: IDS number 703UM

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Cite this

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title = "Time-frequency analysis of chaotic systems",

abstract = "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.",

author = "C Chandre and SR Wiggins and T Uzer",

note = "Publisher: Elsevier Science BV Other identifier: IDS number 703UM",

year = "2003",

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doi = "10.1016/S0167-2789(03)00117-9",

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T1 - Time-frequency analysis of chaotic systems

AU - Chandre, C

AU - Wiggins, SR

AU - Uzer, T

N1 - Publisher: Elsevier Science BV Other identifier: IDS number 703UM

PY - 2003/7

Y1 - 2003/7

N2 - 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.

AB - 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.

U2 - 10.1016/S0167-2789(03)00117-9

DO - 10.1016/S0167-2789(03)00117-9

M3 - Article (Academic Journal)

VL - 181 (3-4)

SP - 171

EP - 196

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -

Time-frequency analysis of chaotic systems

Abstract

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