Intermittent chaos in three-body dynamics

New Astronomy Reviews

Volumn 42, Issue 1, 1998, Pages 41-66

  Chernin, Arthur D ^a   Valtonen, Mauri J ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF TURKU   (Finland)

Author keywords

Celestial mechanics; Dynamical chaos; Stellar dynamics

Indexed keywords

EID: 0032114402     PISSN: 13876473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1387-6473(98)00021-9     Document Type: Article

References (55)

1. Aarseth, S.J., 1963, MNRAS, 126, 223.
2. Aarseth, S.J., Anosova J.P., Orlov V.V., & Szebehely V.G., 1994, Celest. Mech. Dyn. Astron. 58, 1.
3. Agekian, T.A. & Anosova, J.P., 1967, SvA, 44, 1261.
4. Alekseev, V.M., 1969, Math. Sbornik (in Russian) 78, 3.
5. Alekseev, V.M., 1981, Am. Math. Soc. Transl. 2, 112.
6. Anosova, J.P., 1985, Totals of Science and Technology, Ser. Astron. 26, 57.
7. Anosova, J.P., Kiseleva, L.G., Orlov, V.V., & Chernin, A.D., 1991a, SvA, 68, 449.
8. Anosova, J.P., Kiseleva, L.G., Ivanov, A.V., Orlov, V.V., & Chernin, A.D., 1991b, SvA, 69, 461.
9. Antonov, V.A. & Chernin, A.D., 1993, AstL, 19, 312.
10. Arnold, V.I., 1978, Mathematical Methods of Classical Mechanics, Springer-Verlag, Heidelberg.
11. Arnold, V.I., 1963, Russ. Math. Surv. 18, 9, Springer-Verlag, Heidelberg.
12. Chernin, A.D. & Ivanov, A.V., 1990, in: Paired and Interacting Galaxies, NASA, p. 651.
13. Chernin, A.D. & Mikkola, S., 1991, MNRAS, 253, 153.
14. Chernin, A.D., Ivanov, A.V., Trofimov, A.V., & Mikkola, S., 1994, A&A, 281, 685.
15. Chernin, A.D., Heinämäki, P., Lento, H., & Valtonen, M.J., 1997, in press.
16. Contopoulos, G., 1985, in: Chaos in Astrophysics, eds. J.R. Buhler et al., D. Reidel, Dordrecht, p. 259.
17. Contopoulos, G., 1963, AJ, 68, 1.
18. Dubois, M., Rubio, M.A., & Bergé, P., 1983, PhRvL, 51, 1446.
19. Fermi, E., Pasta, J., & Ulam, S., 1954, in: Fermi, E., Collected Works, Vol. II, Acad. Nat. Linc., Rome, p. 978.
20. Galgani, L., 1985, in: Chaos in Astrophysics, eds. J.R. Buhler et al., D. Reidel, Dordrecht, p. 245.
21. Grassberger, P. & Procaccia, I., 1983, PhRvL, 50, 448.
22. Hao, B.L., 1989, Chaos, World Scientific Publ., Singapore.
23. Hanon, M. & Heiles, C., 1964, AJ, 69, 73.
24. Hietarinta, J. & Mikkola, S., 1993, Chaos 3 (2), 183.
25. Ivanov, A.V. & Chernin, A.D., 1991, SvAL, 17, 569.
26. Ivanov, A.V., Filistov, E.A., & Chernin, A.D., 1995, ARep, 39, 368.
27. Karachentsev, I.D., Karachentseva, V.E., & Lebedev, V.S., 1989, Izvestia Special Astrophys, Observ. 27, 67.
28. Karachentsev, I.D., Byrd, G.G., Chernin, A.D., & Valtonen, M.J., 1997, FCPh, in press.
29. Kiseleva, L.G. & Chernin, A.D., 1988, SvAL, 14, 412.
30. Kiseleva, L.G. & Chernin, A.D., 1989, SAO Rep. 60, 5.
31. Kolmogorov, A.N., 1954, Dokl. Acad. Nauk SSSR 98, 527.
32. Kolmogorov, A.N., 1959, Dokl. Acad. Nauk SSSR 124, 754.
33. Lehto, H.J., Czerny, B., & McHardy, M., 1993, MNRAS, 216, 125.
34. Li, T.-Y. & Yorke, J., 1975, Amer. Math. Month. 82, 985.
35. Lorentz, E.N., 1963, J. Atmosph. Sci. 20, 130.
36. Mandelbrot, B.B., 1982, The Fractal Geometry of Nature, Freeman, San Francisco.
37. Manneville, P. & Pomeau, Y., 1980, Comm. Math. Phys. 74, 189.
38. Marchal, C., 1990, The Three-Body Problem (Studies in Astronautics 4), Elsevier, Amsterdam.
39. Mikkola, S., 1994, NMRAS, 269, 127.
40. Nemytskii, V.V. & Stepanov, V.V., 1949, Qualitative Theory of Differential Equations (in Russian), Gostehizdat, Moscow.
41. Ott, E., 1993, Chaos in Dynamical Systems, Cambridge Univ. Press, Cambridge.
42. Poincaré, A., 1899, Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villards, Paris.
43. Ruelle, D. & Takens, F., 1971, Comm. Math. Phys. 23, 343.
44. Sagdeev, R.Z., Usikov, D.A., & Zaslavsky, G.M., 1988, Nonlinear Physics: From the Pendulum to Turbulence and Chaos, Harwood Acad. Publ., New York.
45. Simó, C., 1982, in: Classical Mechanics and Dynamical Systems, eds. R. Devaney et al., Marcel Dekker, New York, p. 203.
46. Szebehely, V., 1972, A&A, 77, 169.
47. Valtonen, M.J., 1988, VA, 32, 23.
48. Valtonen, M.J. & Mikkola, S., 1991, ARA&A, 29, 9.
49. Valtonen, M.J., Mikkola, S., & Pietilä, H., 1995, MNRAS, 273, 751.
50. Valtonen, M.J., Mikkola, S., Heinämäki, & Valtonen, H., 1994, ApJS, 95, 69.
51. Wiren, S., Zheng, Q.-J., Valtonen, M.J., & Chernin, A.D., 1996, ApJ, 111, 160.
52. Wintner, A., 1941, The Analytical Foundations of Celestial Mechanics, Princeton Univ. Press, Princeton, NJ.
53. Zaslavsky, G.M., 1985, Chaos in Dynamical Systems, Harwood Acad. Publ., New York.
54. Zaslavsky, G.M., Sagdeev, R.Z., Cherninkov, A.A., & Usikov, D.A., 1991, Weak Chaos and Quasiregular Patterns, Cambridge Univ. Press, New York.
55. Zheng, Q.-J., Valtonen, M.J., & Chernin, A.D., 1993, ApJ, 105, 2047.