A solution to the problem posed by Byland and Scialom

Abstract

Recently, Byland and Scialom studied the evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs universe on the basis of dynamical systems methods (Phys. Rev. D57, 6065 (1998), gr-qc/9802043). In particular, they have pointed out a problem to determine the stability properties of one of the degenerate critical points of the corresponding dynamical system. Here we give a solution, showing that this point is unstable both to the past and to the future. We also discuss the asymptotic behavior of the trajectories in the vicinity of another critical point.