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Integrable Third and Fifth Order Dynamical Systems with Dissipation

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We establish the integrability of some homogeneous (with respect to a part of variables) dynamical systems of odd (third and fifth) order. In the class of such systems, we extract… Click to show full abstract

We establish the integrability of some homogeneous (with respect to a part of variables) dynamical systems of odd (third and fifth) order. In the class of such systems, we extract a system on the tangent bundle of smooth manifolds. The force field is separated into the internal (conservative) force field and the external force field with alternating dissipation. The external force field is introduced by using a certain unimodular transformation and generalizes the cases studied by the author earlier.

Keywords: force field; fifth order; third fifth; dynamical systems

Journal Title: Journal of Mathematical Sciences
Year Published: 2019

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