Locally \(U(1)\times U(1)\) symmetric cosmological models: Topology and dynamics (Q2710228)

The locally \(U(1)\times U(1)\) symmetric cosmological models (or the generalized Gowdy models) are characterized by the existence of two commuting spatial local Killing vectors. The author presents a classification of possible spatial topologies in this class. The significance of the locally homogeneous limit of the model is emphasized. Next the author presents a method of reduction to the natural reduced manifold and analyzes the equivalences at the reduced level of the models as dynamical systems. Finally, he obtains the translation and reflection operators which commute with the dynamical flow in the phase space.