On the Existence of Local Integrals of Motion in the Dynamics of Stellar Systems

Abstract The existence of the local integrals of motion is investigated in steady-state rotating stellar systems with two degrees of freedom. A class of gravitational potentials is constructed that admit local integrals, linear and quadratic in the velocity components. It is shown that the presence of such integrals reduces the order of the system of differential equations of motion, constrains mixing in phase space, and facilitates the formation of dynamically isolated subsystems. The results enhance the understanding of gravitational system dynamics and may be applied to studies of stability and evolution, including those of dense stellar systems.

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