Gurzadyan, V. G.; Savvidy, G. K., Collective relaxation of stellar systems,
Astronomy and Astrophysics (A&A), vol. 160, p. 203-210, 1986
; available freely at


Brief version: Gurzadian, V. G.; Savvidi, G. K. Problem of the relaxation of stellar systems, Doklady AN SSSR, 277, 69, 1984.pdf (Communicated by V.

In this paper the exponential instability (chaos) of spherical stellar systems was proved and the collective relaxation time has been derived using methods of ergodic theory. The obtained value of the relaxation time removed the Zwicky paradox for elliptical galaxies known many decades, according to which the two-body relaxation time exceeds their age, i.e. they still have to be unrelaxed.

The derived relaxation formula has been shown to fit the observations 
(Vesperini, E., Possible observational indication for Gurzadyan-Savvidyrelaxation for globular clusters, A&A, 266, 215, 1992), numerical experiments (El-Zant, A. A., On the stability of motion of N-body systems: a
geometric approach, A&A, 331, 782, 1998) and was reconfirmed via van Kampen 
stochastic equation technique (Gurzadyan, V. G.; Kocharyan, A. A.,Collective relaxation of stellar systems revisited, A&A,505,625, 2009).

That relaxation formula is given in handbook K.Lang, Astrophysical Formulae,
Springer, 1999, is quoted in over dozen textbooks and monographs on chaos and on stellar dynamics.