  A detailed analysis of the phase trajectories of cosmological models based on
classical and scalar fields near surfaces of zero effective energy has been
carried out. A study of the differential parameters of the convergence of phase
trajectories to a zero-energy surface boundary shows that the phase
trajectories merge within a finite time with the phase trajectories of free
oscillations corresponding to zero effective energy. This confirms the
assumption formulated in a number of previous works by one of the authors about
the existence of Euclidean limit cycles in cosmological models based on scalar
fields with a Higgs interaction potential.
