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Volumn 55, Issue 3, 1997, Pages 2722-2735

Geometric interpretation of chaos in two-dimensional hamiltonian systems

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; LYAPUNOV METHODS; MATRIX ALGEBRA; OSCILLATIONS; PERTURBATION TECHNIQUES;

EID: 0031221414     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2722     Document Type: Article
Times cited : (15)

References (27)
  • 1
    • 85037238872 scopus 로고    scopus 로고
    • Cf. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960)
    • Cf. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960);
  • 3
    • 85037199458 scopus 로고    scopus 로고
    • Cf. E. Hopf, Trans. Am. Math. Soc. 39, 229 (1936)
    • Cf. E. Hopf, Trans. Am. Math. Soc. 39, 229 (1936).
  • 7
    • 5544294701 scopus 로고
    • Astrophys. J. 364, 420 (1990).ASJOAB
    • (1990) Astrophys. J. , vol.364 , pp. 420
  • 12
    • 0000456667 scopus 로고    scopus 로고
    • Cf. J. N. Mather, Topology 21, 457 (1982)
    • Cf. J. N. Mather, Topology 21, 457 (1982);
  • 18
    • 85037178760 scopus 로고    scopus 로고
    • 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
    • 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.
  • 19
    • 0039971037 scopus 로고    scopus 로고
    • 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
    • (1996) Phys. Rev. E , vol.53 , pp. 5473
    • Habib, S.1    Kandrup, H.E.2    Mahon, M.E.3
  • 20
    • 26744464510 scopus 로고    scopus 로고
    • 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
    • (1997) Astrophys. J. , vol.480 , pp. 155
  • 22
    • 35949037738 scopus 로고
    • Cf. G. Bennetin, L. Galgani, and J.-M. Strelcyn, Phys. Rev. A 14, 2338 (1976).PLRAAN
    • (1976) Phys. Rev. A , vol.14 , pp. 2338
    • Galgani, L.1
  • 23
    • 0001399722 scopus 로고
    • Cf. G. Contopoulos, Astron. J. 76, 147 (1971) or ANJOAA
    • (1971) Astron. J. , vol.76 , pp. 147
  • 25
    • 85037238156 scopus 로고    scopus 로고
    • Cf. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992)
    • Cf. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992).
  • 26
    • 85037200070 scopus 로고    scopus 로고
    • Cf. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965)
    • Cf. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.