Long-term evolution of spheroidal galaxies with locally isotropic velocity distribution

The short-term evolution of spheroidal galaxies has been explored by S. Chandrasekhar et al. and G. S. Sunder et al. In this paper, we study their long-term evolution with Laskar's method of frequency analysis. The main new results are as follows: (1) There exists a unique equilibrium, which is spherically symmetric. This equilibrium has a critical linear stability. (2) Generally speaking, the semi-axes exhibit quasiperiodic or nearly quasi-periodic (in a time scale longer than a Hubble time) oscillations around the radius of the above-mentioned equilibrium, so the equilibrium is practically stable. (3) There are cases in which one of the semi-axes tends fast to zero while the other to some finite value. The limit state is generally planar rather than linear, i.e. it is the symmetric semi-axis that tends to zero. This implies that some disk galaxies may have originated from spheroidal pregalaxy material.