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[Integrable Hamiltonian systems with noncompact foliations and bifurcations] В. А. Кибкало |
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Аннотация: Topological classification of integrable Hamiltonian systems developed by A. Fomenko and his school was applied to a wide class of geometrical, mechanical and physical systems. Compactness of fibers of their Liouville foliations is an important assumption here. Else new effects arise: incomplete Hamiltonian flows, non-critical bifurcations (bifurcation value preimage doesn’t contain critical points of the momentum map, moreover, it can be empty). We will discuss several results on such systems (see survey by A. Fomenko, D. Fedoseev, 2020 J.Math.Sc.). Note that effects related to "noncompactness" appeared in a more general context of dynamical systems, more precisely, as connections between nonautonomous vector fields and diffeomorphisms (V.Grines, L.Lerman, 2022-2023). Pseudo-Euclidean analogues of rigid body dynamics (see A. Borisov, I. Mamaev, 2016) turn out to be an important class of systems with noncompact foliations. New our results on topology of Liouville foliations of pseudo-Euclidean Euler, Lagrange and Kovalevskaya tops, Zhukovsky and Klebsch systems will be presented. Both compact and non-compact fibers, their bifurcations (including non-critical one) appear in such systems. Bifurcations and Liouville foliations bases (analogs of Fomenko graphs) are also determined. Язык доклада: английский Website: https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09 |
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