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A complete model of cosmological evolution of a classical scalar field withthe Higgs potential is studied and simulated on a computer without assumptionthat the Hubble constant is nonnegative. The corresponding dynamical system isqualitatively analyzed and the Einstein-Higgs hypersurfaces the topology ofwhich determines the global properties of the phase trajectories of thecosmological model are classified.

Complete model of cosmological evolution of a classical scalar field with the Higgs potential. I. Analysis of the model