Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-19T12:44:23.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Vector Laypunov Functionals and Stabilities and Chaoticities of Functional Differential Equations Occurring in Celestial Mechanics and Stellar Dynamics

Published online by Cambridge University Press:  12 April 2016

D.R.K. Sastry
D.R.K. Sastry*
Affiliation:
Research Centre for Advanced Studies, Kondapur, Opp:Central University, Hyderabad - 500133, India

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Vector laypunov functions and stabilities and chaoticities of Functional Differential Equations occurring in Celestial Mechanics and Stellar Dynamics have been discussed. Fuzzy dynamical systems are more realistic while considering problems occurring in Celestial Mechanics and Stellary Dynamics.

Type
Part I Chaos
Information
International Astronomical Union Colloquium , Volume 132: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics , 1993 , pp. 61 - 65
Copyright
Copyright © Nova Science Publishers 1993

References

[1] Grebenikov, E.A. and Ryabov, Yu. A, Constructive methods in the Nonlinear Analysis of Nonlinear Systems, MIR pub1ishers, 1983.Google Scholar
[2] Gurevich, L.E. and A.D., Chernin, The Magic of Galaxies and Stars, MIR Publishers, Moscow, 1987.Google Scholar
[3] Jack Hale, , Theory of Functional Differential Equations, Springers, 1987.Google Scholar
[4] La Salle, J.P., Vector Laypunov Functions, LCDS Tech.Rep. ≠ 75-1, Brown University, Prodince, RI, USA, 175.Google Scholar
[5] i) May, R.M., Biological populations with non-overlapping generations, Stable points, Stable cycles and Chaos, Science, 186, 645–647, 1974.Google Scholar
ii) May, R.M., Simple Mathematical Models with very comlicated dynamics, Natture, 261, 459–467, 1976.Google Scholar
[6] Handbook on Celestial Mechanics and Astrodynamics, Nauk, Moscow, 1975.Google Scholar
[7] Duboshin, G.N, Basic Problems and Methods of Celestial Mechanics, Nauk, Moscow, 1975.Google Scholar
[8] Bogoliubo, N.N. and Mitropolskii, Yu.A., Asymptotic Methods in the theory of nonlinear oscillations, Fizmatgiz, Moscow, 1963.Google Scholar
[9] Arnold, V.I, Mathematical methods in classical mechanics, Nauk, Moscow, 1974.Google Scholar
[10] Arnold, V.I., Russian Mathematical Surveys, 18(9), 1963.Google Scholar
[11] Moser, J., Recent developments in the theory of Hamiltonian systems, SIAM Reviews, 28, 459, 1986.Google Scholar
[12] Celletti, A., Spin-Orbit resonances in Celestial Mechanics, ZAMP, 41, 1990 and the references contained therein.Google Scholar
[13] Li, T-Y, Yorke, J.A., Period three implies chaos, Amer. Math, Monthly, 82, 985–992, 1975.Google Scholar
[14] James, Hurt, Stability theorems for difference equations, LCDS Tech, Rep. ≠ 66-6, Brown University, Providence, RI, USA, 1966.Google Scholar
[15] Bellman, R., Bentsman, J. and Meerkov, S.M., Nonlinear Systems with Fast Parametric Oscillations. J1. Math. Anal. Applns. 57, 572–589 (1983).Google Scholar
[16] Stephen Wiggins, , Global Bifurcations and Chaos, Springers, 1988.Google Scholar