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

Classical and Quantum Gravity

Volumn 21, Issue 3, 2004, Pages

  Vela Arevalo, Luz V ^a   Marsden, Jerrold E ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1142266386     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/21/3/022     Document Type: Article

References (27)

1. Vela-Arevalo L V and Wiggins S 2001 Time-frequency analysis of classical trajectories of polyatomic molecules Int. J. Bifurcation Chaos 11 1359-80
2. Tsiganis K, Varvoglis H and Hadjidemetriou J D 2000 Stable chaos in the 12:7 mean motion resonance and its relation to the stickiness effect Icarus 146 240-52
3. Koon W S, Lo M W, Marsden J E and Ross S D 2000 Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics Chaos 10 427-69
4. Ross S D, Koon W S, Lo M W and Marsden J E 2003 Design of a multi-moon orbiter AAS 03-143
5. Dellnitz M, Junge O, Koon W-S, Lekien F, Lo M W, Marsden J E, Padberg K, Preis R, Ross S D and Thiere B 2003 Transport in dynamical astronomy and multibody problems Preprint
6. Lichtenberg A J and Lieberman M A 1983 Regular and Chaotic Dynamics (New York: Springer)
7. Contopoulos G and Voglis N 1997 A fast method for distinguishing between ordered and chaotic orbits Astron. Astrophys. 317 73-81
8. Froeschlé C and Lega E 1998 Twist angles: a method for distinguishing islands, tori and weak chaotic orbits. Comparison with other methods of analysis Astron. Astrophys. 334 355-62
9. Laskar J, Froeschlé C and Celletti A 1992 The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping Physica D 56 253-69
10. Laskar J 1993 Frequency analysis for multi-dimensional systems. Global dynamics and diffusion Physica D 67 257-81
11. Binney J and Spergel D 1982 Spectral stellar dynamics Astrophys. J. 251 308-21
12. Martens C and Ezra G 1987 Classical and semiclassical mechanics of strongly resonant systems - a Fourier transform approach J. Chem. Phys. 86 279-307
13. Laskar J 1990 The chaotic motion of the solar system: a numerical estimate of the size of the chaotic zones Icarus 88 226-91
14. Losada J C, Estebaranz J M and Benito R M 1998 Local frequency analysis and the structure of classical phase space of the LiNC/LiCN molecular system J. Chem. Phys. 108 63-71
15. Szebehely V 1967 Theory of Orbits (New York: Academic)
16. Arnold V I 1963 Proof of a theorem by A N Kolmogorov on the persistence of quasiperiodic motions under small perturbations of the Hamiltonian Russ. Math. Surv. 18 9-36
17. Arnold V I 1963 Small denominators and problems of stability of motion in classical and celestial mechanics Russ. Math. Surv. 18 85-191
18. Vakman D 1996 On the analytic signal, the Teager-Kaiser energy algorithm, and other methods for defining amplitude and frequency IEEE Trans. Signal Process. 44 791-7
19. Mandel L 1974 Interpretation of instantaneous frequency Am. J. Phys. 42 840-6
20. Gabor D 1946 Theory of communications J. IEE 93 429-57
21. Ville J 1948 Théorie et applications de la notion de signal analytique Cables Transm. 2 61-74
22. Forstneric F 1996 Actions of (ℝ, +) and (ℂ, +) on complex manifolds Math. Z. 223 123-53
23. Delprat N, Escudié B, Guillemain P, Kronland-Martinet R, Thamitchian P and Torrésani B 1992 Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies IEEE Trans. Inf. Theory 38 644-64
24. Vela-Arevalo L V 2002 Time-frequency analysis based on wavelets for Hamiltonian systems PhD Thesis California Institute of Technology
25. Carmona R, Hwang W and Torrésani B 1998 Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S (San Diego, CA: Academic)
26. Daubechies I 1992 Ten Lectures on Wavelets (Philadelphia, PA: SIAM)
27. Copson E T 1965 Asymptotic Expansions (Cambridge: Cambridge University Press)