Abstract
This paper is concerned with the problem of three vortices on a sphere S2 and the Lobachevsky plane L2. After reduction, the problem reduces in both cases to investigating a Hamiltonian system with a degenerate quadratic Poisson bracket, which makes it possible to study it using the methods of Poisson geometry. This paper presents a topological classification of types of symplectic leaves depending on the values of Casimir functions and system parameters.
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