Time-Frequency Analysis of the Restricted Three-Body Problem: Transport and Resonance Ttransitions

Vela-Arevalo, L. and J. E. Marsden

Classical and Quantum Gravity , 21, S351-S375

Abstract:

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.