This article is cited in 11 papers

The topology of Liouville foliation for the Sokolov integrable case on the Lie algebra so(4)

G. Haghighatdoost^a, A. A. Oshemkov<sup>b

a</sup> Department of Fundamental Sciences, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Several new integrable cases for Euler's equations on some six-dimensional Lie algebras were found by Sokolov in 2004. In this paper we study topological properties of one of these integrable cases on the Lie algebra so(4). In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, the classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.
Bibliography: 9 titles.

Keywords: integrable Hamiltonian systems, momentum mapping, bifurcation diagram, topological invariants.

UDC: 517.938.5

MSC: 37J35, 70H06

Received: 25.12.2007 and 16.03.2009

DOI: 10.4213/sm4501

 English version: Sbornik: Mathematics, 2009, 200:6, 899–921

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