On periodic solutions of the restricted three-dimensional three-body problem (Q1382605)

The paper deals with a spatial three-body problem proposed by A. N. Kolmogorov. Two equal masses describe in plane \((x,y)\) elliptical orbits symmetrical with respect to the \(z\)-axis, while the third point with zero mass remains on the \(z\)-axis. The author establishes conditions for existence of an infinite number of non-degenerate long-periodic solutions accumulated in a neighbourhood of the separatrix of nonperturbed motion.