Effects of dynamical friction on star orbits in a spherical cluster uniformly rotating with small angular velocity about a fixed axis are considered, deformations of the cluster due to the rotation being neglected. The test star is supposed to move in a noncircular restricted orbit under the influence of both the attraction of the cluster with the smoothed-out distribution of stellar matter and dynamical friction due to random encounters of the test star with other stars of the cluster.

The approximate formula for dynamical friction has been deduced, the encounters being supposed to be the binary ones. The differential equations for the osculating elements of the star orbit have been obtained for the two cases of the density distribution - the uniform and the exponential ones. The numerical results demonstrate the complicated character of dynamical friction effects on the evolution of the orbit. The orbit tends to become circular, and its inclination decreases. These effects are proportional to the mass of the test star. This leads to the conclusion that dynamical friction contributes noticeably to the concentration of massive stars near the center of the cluster.

We continue to study the number of isolating integrals in dynamical systems with three and four degrees of freedom, using as models the measure preserving mappings T already introduced in previous papers (Froeschlé, 1972; Froeschlé and Scheidecker, 1973a).

Thus, we use here a new numerical method which enables us to take as indicator of stochasticity the variation with n of the two (respectively three) largest eigenvalues - in absolute magnitude - of the linear tangential mapping Tn∗ of Tn. This variation appears to be a very good tool for studying the diffusion process which occurs during the disappearance of the isolating integrals, already shown in a previous paper (Froeschlé, 1971). In the case of systems with three degrees of freedom, we define and give an estimation of the diffusion time, and show that the gambler's ruin model is an approximation of this diffusion process.