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1
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85037238872
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Cf. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960)
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Cf. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960);
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3
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85037199458
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Cf. E. Hopf, Trans. Am. Math. Soc. 39, 229 (1936)
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Cf. E. Hopf, Trans. Am. Math. Soc. 39, 229 (1936).
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7
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5544294701
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Astrophys. J. 364, 420 (1990).ASJOAB
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(1990)
Astrophys. J.
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12
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0000456667
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Cf. J. N. Mather, Topology 21, 457 (1982)
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Cf. J. N. Mather, Topology 21, 457 (1982);
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14
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0001286323
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M. E. Mahon, R. A. Abernathy, B. O. Bradley, and H. E. Kandrup, Mon. Not. R. Astron. Soc. 275, 443 (1995).MNRAA4
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(1995)
Mon. Not. R. Astron. Soc.
, vol.275
, pp. 443
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Mahon, M.E.1
Abernathy, R.A.2
Bradley, B.O.3
Kandrup, H.E.4
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18
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85037178760
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This is of special interest physically given the fact that, for a system like a galaxy, (Formula presented) corresponds to a period of time comparable to the age of the Universe
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This is of special interest physically given the fact that, for a system like a galaxy, (Formula presented) corresponds to a period of time comparable to the age of the Universe.
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19
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0039971037
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In certain cases, e.g., for chaotic orbits trapped by cantori near regular islands, it is not easy to determine whether or not a given segment is in fact chaotic. To make precise determination in such potentially ambiguous cases, the segment was integrated for significantly longer times (Formula presented) to see whether the computed short time Lyapunov exponent (Formula presented) eventually begins to increase and/or whether, in configuration space, the segment eventually moves away from the regular island. When even such longer time integrations were inconclusive, the orbits were reintegrated in the presence of very weak additive white noise since [cf. S. Habib, H. E. Kandrup, and M. E. Mahon, Phys. Rev. E 53, 5473 (1996); PLEEE8
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(1996)
Phys. Rev. E
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, pp. 5473
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Habib, S.1
Kandrup, H.E.2
Mahon, M.E.3
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20
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26744464510
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Astrophys. J. 480, 155 (1997)] such perturbations tend to decrease dramatically the time scale on which chaotic orbits diffuse through cantori without allowing regular orbits to breach true KAM tori.ASJOAB
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(1997)
Astrophys. J.
, vol.480
, pp. 155
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22
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35949037738
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Cf. G. Bennetin, L. Galgani, and J.-M. Strelcyn, Phys. Rev. A 14, 2338 (1976).PLRAAN
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(1976)
Phys. Rev. A
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Galgani, L.1
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23
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0001399722
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Cf. G. Contopoulos, Astron. J. 76, 147 (1971) or ANJOAA
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Astron. J.
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25
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85037238156
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Cf. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992)
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Cf. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992).
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26
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85037200070
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Cf. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965)
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Cf. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965).
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