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Precessional switching and relaxation in a single-domain particle or film is studied by using the Landau-Lifshitz-Gilbert equation. The analysis of the switching process is based on the explicit knowledge of two integrals of motion for the magnetization dynamics in the conservative case. The knowledge of these integrals of motions enables one to carry out the geometrical analysis of the system and give the complete phase portrait. The relaxation process which occurs after the magnetization is reversed is analyzed by using geometrical methods and it is showed that the dynamical system exhibits entanglement of separatrices and riddled basins of attraction.