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Time-frequency analysis of the restricted three-body problem: transport and resonance transitions

Vela-Arevalo, Luz V. and Marsden, Jerrold E. (2004) Time-frequency analysis of the restricted three-body problem: transport and resonance transitions. Classical and Quantum Gravity, 21 (3). S351-S375. ISSN 0264-9381.

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A method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem.. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space.

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Additional Information:© Institute of Physics and IOP Publishing Limited 2004. Received 21 October 2003. Published 13 January 2004. Print publication: Issue 3 (7 February 2004). Dedicated to Vince Moncrief on the occasion of his 60th birthday. The research of LVV-A was partially supported by CONACYT Mexico and by the J Ford Fellowship, GaTech. The research of JEM was partially supported by NSF grant DMS-0204474 and by a Max Planck Research Award.
Subject Keywords:instantaneous frequencies, chaotic orbits, mechanics, systems
Issue or Number:3
Record Number:CaltechAUTHORS:VELcqg04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:864
Deposited By: Tony Diaz
Deposited On:31 Oct 2005
Last Modified:02 Oct 2019 22:37

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