Bifurcation diagrams of natural Hamiltonian systems on Bertrand manifolds / D. A. Fedoseev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 1. P. 62-65 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 44-47].

Bifurcation diagrams for natural integrable Hamiltonian systems on Bertrand manifolds (i.e., on configuration spaces of one inverse problem of dynamics) are constructed. Some properties of the corresponding Liuoville foliations are studied, namely, the compactness and the number of foliation components in the preimage under momentum map.

Key words: Bertrand's Riemannian manifold, surface of revolution, Hamiltonian systems, bifurcation diagram.

№ 1/2015