Abstract
A connection is shown to exist between the Gaussian curvature of the associated manifold and the ergodic or non-ergodic behaviour of certain dynamical systems of astronomical and astrophysical importance.
Similar content being viewed by others
References
Abramowitz, M. and Stegun, I.: 1964,Handbook of Mathematical Functions. Dover Publ., New York.
Benettin, G., Galgani, L., and Strelcyn, J. M.: 1976,Phys. Rev. A14, 2338.
Fehlberg, E.: 1969,Computing 4, 93.
Gear, C. W.: 1971,Numerical Initial-Value Problems in Ordinary Differential Equations, Prentice-Hall Inc., New York, p. 158.
Hénon, M. and Heiles, C.: 1964,Astron. J. 69, 73.
Hopf, E.: 1939,Sitzber. Sächsische Akad. Wiss. Leipzig 91, 261.
Poincaré, H.: 1957,Les méthodes nouvelles de la mécanique céleste, Dover (offset republication), Vol.1, p. 83.
Whittaker, E. T.: 1961,A Treatise on the Analytical Dynamics of the Particles and Rigid Bodies, Cambridge University Press, Cambridge.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Evangelidis, E.A., Neethling, J.D. The Gaussian curvature of associated manifold of dynamical systems. Astrophys Space Sci 103, 99–113 (1984). https://doi.org/10.1007/BF00650048
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00650048