Integrals of motion for three-dimensional non-Hamiltonian dynamical systems

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The problem of finding integrals of motion of three-dimensional dynamical systems is analysed. The authors introduce a new type of direct method in the search of parameter values for which an integral of motion exists. This method consists in proposing an ansatz for the integral that explicitly shows the dependence with respect to one of the phase space coordinates of the system. They apply this procedure to the reduced three-wave interaction problem and to the Rabinovich system. For both models new integrals of motion are found.