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Nonlinear Problems in Stellar Dynamics

  • Conference paper
Nonlinear Phenomena in Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 3))

Abstract

We deal with orbits of stars in galaxies (1) on the plane of symmetry of a spiral galaxy (2) on the meridian plane of an axisymmetric galaxy and (3) three-dimensional orbits in non-axisymmetric galaxies. The theory of the “third integral” explains the ordered motions- However, there are also stochastic motions that play an important role near resonances. The transition to stochasticity is studied. Finally some new types of phenomena that appear in 3-dimensional systems are discussed.

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References

  1. C.C. Lin and F.H. Shu: Astrophys. J. 140, 646 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  2. C.C. Lin and Y.Y. Lau: Stud. Appl. Math. 60, 97(1979).

    MathSciNet  ADS  Google Scholar 

  3. A.J. Kalnajs: Astrophys. J. 166, 275 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  4. A. Toomre, in S.M. Fall and D. Lynden-Bell (eds.): The structure and evolution of normal galaxies (Cambridge Univ. Press, Cambridge 1981), p. 113.

    Google Scholar 

  5. G. Contopoulos: Astrophys. J. 201, 566 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  6. G. Contopoulos: Astron. Astrophys. 64, 323 (1978).

    ADS  MATH  Google Scholar 

  7. G. Contopoulos: Z. f. Astrophysik 49, 27 (1960).

    MathSciNet  Google Scholar 

  8. G. Contopoulos and M. Moutsoulas: Astron. J. 70, 817 (1965).

    Article  ADS  Google Scholar 

  9. F.G. Gustavson: Astron. J. 71, 670 (1966).

    Article  ADS  Google Scholar 

  10. M.N. Rosenbluth, R.A. Sagdeev, J.B Taylor and M. Zaslavskii: Fuel. Fusion 6, 297 (1966).

    Google Scholar 

  11. G. Contopoulos, in F. Nahon and M. Hénon (eds.): Les nouvelles méthodes de

    Google Scholar 

  12. la dynamique stellaire (CNRS, Paris, 1966) ≡ Bull. Astron., Ser. 3, 2, Fasc. 1, 223 (1967).

    Google Scholar 

  13. B.V. Chirikov: Phys. Rep. 52, 263 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  14. M. Zaslavskii and B.V. Chirikov: Sov. Phys. Uspekhi 14, 549 (1972).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. J.M. Greene: J. Math. Phys. 20, 1183 (1979).

    Article  ADS  Google Scholar 

  16. R.S. MacKay:, Ph.D. Thesis, Princeton University (1982).

    Google Scholar 

  17. S.J. Shenker and L.P. Kadanoff: J. Stat. Phys. 27, 631 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  18. M.J. Feigenbaum: J. Stat. Phys. 19, 25 (1978).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. P. Coullet and C. Tresser: J. Phys. C 5, 25 (1978).

    Google Scholar 

  20. G. Benettin, C. Cercignani, L. Galgani and A. Giorgilli: Lett. Nuovo Cim. 28, 1 (1980).

    Article  Google Scholar 

  21. J.M. Greene, R.S MacKay, F. Vivaldi and M.J. Feigenbaum: Physica D 3 468 (1981).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. T. Bountis: Physica D 3, 577 (1981).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. G. Contopoulos: Physica D 8, 142 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. G. Contopoulos: Lett. Nuovo Cim. 38, 257 (1983).

    Article  MathSciNet  Google Scholar 

  25. G. Contopoulos: Astron. J. 75, 96; 108 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  26. G. Contopoulos and M. Zikides: Astron. Astrophys. 90, 198 (1980).

    MathSciNet  ADS  Google Scholar 

  27. D.S. Heggie: Celes. Mech. 29, 207 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. R.M. May: Nature 261, 257 (1976).

    Article  Google Scholar 

  29. M. Widom and L.P. Kadanoff: Physica D 5, 287 (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. V.I. Arnold and A. Avez: Ergodic problems of classical mechanics (Benjamin, N. York 1968).

    Google Scholar 

  31. N.N. Nekhoroshev: Russian Math. Surveys 32, 6, 1 (1977).

    Article  ADS  MATH  Google Scholar 

  32. G. Contopoulos, L. Galgani and A. Giorgilli: Phys. Rev. A 18, 1183 (1978).

    Article  ADS  Google Scholar 

The above list is quite incomplete. Important books containing also many references are

  • V.I. Arnold: 1979, Mathematical methods of classical mechanics, Springer Verlag, New York.

    Google Scholar 

  • R.H.G. Helleman (ed.): 1980, Nonlinear dynamics, Ann. N. York Acad. Sci. 357, New York.

    Google Scholar 

  • S. Jorna (ed.): 1978, Topics in nonlinear dynamics, Amer. Inst. Phys. 46, New York.

    Google Scholar 

  • A.J. Lichtenberg and M.A. Lieberman: 1983, Regular and stochastic motion, Springer Verlag, New York.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. European Southern Observatory, D-8046, Garching bei München, Fed. Rep. of Germany

    G. Contopoulos

Authors
  1. G. Contopoulos
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Editor information

Editors and Affiliations

  1. Facultad de Fisica, Pontificia Universidad Catolica de Chile, Casilla 114-D, Santiago, Chile

    Francisco Claro Ph.D.

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© 1985 Springer-Verlag Berlin Heidelberg

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Contopoulos, G. (1985). Nonlinear Problems in Stellar Dynamics. In: Claro, F. (eds) Nonlinear Phenomena in Physics. Springer Proceedings in Physics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93289-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-93289-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-93291-5

  • Online ISBN: 978-3-642-93289-2

  • eBook Packages: Springer Book Archive

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