It is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically\noriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural\nnotion of symmetry for cocycles. It is discussed the fundamental relationship between the existence\nof solutions of cohomological equations and the behavior of the cocycles along periodic orbits. The\ngeneralization of this theorem to a class of suspension flows is also discussed and proved. This\ngeneralization allows giving a different proof of the Livschitz Theorem for flows based on the\nconstruction of Markov systems for hyperbolic flows.
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