Astrophysics and Space Science

, Volume 135, Issue 2, pp 307–324 | Cite as

Relative chaos in stellar systems

  • V. G. Gurzadyan
  • A. A. Kocharyan


Statistical properties of many-dimensional dynamical systems-stellar systems of different types, are investigated by means of new definition of relative chaos based on the estimation of the Ricci curvature in the direction of the velocity of geodesics. Numerical experiment is performed to calculate the Ricci and scalar curvatures for systems with equal total energy. The results of calculations enable one to obtain schematic classification of stellar systems by increasing degree of chaos.


Total Energy Numerical Experiment Schematic Classification Scalar Curvature Ricci Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Anosov, D. V.: 1967,Comm. MIAN SSSR 90.Google Scholar
  2. Arnold, V. I.: 1979,Mathematical Methods of Classical Mechanics, Nauka, Moscow (in Russian).Google Scholar
  3. Benettin, G., Galgani, L., and Strelcyn, J. M.: 1978,Phys. Rev. A 14, 2338.Google Scholar
  4. Bunimovich, L. A.: 1985,Zh. Experim. Teor. Fiz. 89, 1452.Google Scholar
  5. Chirikov, B. V.: 1979,Phys. Reports 52, 263.Google Scholar
  6. Contopoulos, G.: 1984, ESO Preprint, No. 342.Google Scholar
  7. Contopoulos, G., Galgani, L., and Giorgilli, A.: 1978,Phys. Rev. A 18, 1183.Google Scholar
  8. Eneev, T. M., Kozlov, N. N., and Sunyaev, R. A.: 1973,Astron. Astrophys. 22, 41.Google Scholar
  9. Fermi, E., Pasta, J. R., and Ulam, S.: 1955, Los Alamos Rept., LA-1940.Google Scholar
  10. Gromoll, D., Klingenberg, W., and Meyer, W.: 1968,Riemannsche Geometrie in Grossen, Springer-Verlag, New York.Google Scholar
  11. Gurzadyan, V. G.: 1987, ‘Chaos and Order in the Universe’, inParticles and Cosmology, Moscow, Publ. AN SSSR, p. 45.Google Scholar
  12. Gurzadyan, V. G. and Kocharyan, A. A.: 1986a,Dokl. AN SSSR 287, 813.Google Scholar
  13. Gurzadyan, V. G. and Kocharyan, A. A.: 1986b,Dokl. AN SSSR 289, 60.Google Scholar
  14. Gurzadyan, V. G. and Kocharyan, A. A.: 1986c, EPI-971 (68), Yerevan.Google Scholar
  15. Garzadyan, V. G., Kocharyan, A. A., and Matinyan, S. G.: 1986, EPI-825 (3);Dokl. AN SSSR (in press).Google Scholar
  16. Gurzadyan, V. G., and Savvidy, G. K.: 1984,Dokl. AN SSSR 277, 69.Google Scholar
  17. Gurzadyan, V. G. and Savvidy, G. K.: 1986,Astron. Astrophys. 160, 203.Google Scholar
  18. Hénon, M. and Heiles, C.: 1964,Astron. J. 69, 73.Google Scholar
  19. Lichtenberg, A. J. and Lieberman, M. A.: 1983,Regular and Stochastic Motion, Springer-Verlag, New York.Google Scholar
  20. Norman, C. A., May, A., and Van Albada, T. S.: 1985,Astrophys. J. 296, 20.Google Scholar
  21. Pesin, Ya. B.: 1977,UMN,XXXII, 55.Google Scholar
  22. Besin, Ya. B.: 1981,UMN XXXVI, 3.Google Scholar
  23. Weinberg, S.: 1972,Gravitation and Cosmology, Wiley, New York.Google Scholar
  24. Zaslavsky, G. M.: 1984,Stochasticity of Dynamical Systems, Nauka, Moscow (in Russian).Google Scholar

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • V. G. Gurzadyan
    • 1
  • A. A. Kocharyan
    • 1
  1. 1.Department of Theoretical PhysicsYerevan Physics InstituteYerevanArmenia, U.S.S.R.

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