# Topological features of the Sokolov integrable case on the Lie algebra so(3,1)

## Abstract

The integrable Sokolov case on so(3,1){sup ⋆} is investigated. This is a Hamiltonian system with two degrees of freedom, in which the Hamiltonian and the additional integral are homogeneous polynomials of degrees 2 and 4, respectively. It is an interesting feature of this system that connected components of common level surfaces of the Hamiltonian and the additional integral turn out to be noncompact. The critical points of the moment map and their indices are found, the bifurcation diagram is constructed, and the topology of noncompact level surfaces is determined, that is, the closures of solutions of the Sokolov system on so(3,1) are described. Bibliography: 24 titles.

- Authors:

- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22364911

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 8; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; BIFURCATION; DEGREES OF FREEDOM; DIAGRAMS; HAMILTONIANS; INTEGRAL CALCULUS; INTEGRALS; LIE GROUPS; MATHEMATICAL SOLUTIONS; POLYNOMIALS; SO GROUPS; TOPOLOGY

### Citation Formats

```
Novikov, D V.
```*Topological features of the Sokolov integrable case on the Lie algebra so(3,1)*. United States: N. p., 2014.
Web. doi:10.1070/SM2014v205n08ABEH004412.

```
Novikov, D V.
```*Topological features of the Sokolov integrable case on the Lie algebra so(3,1)*. United States. doi:10.1070/SM2014v205n08ABEH004412.

```
Novikov, D V. Sun .
"Topological features of the Sokolov integrable case on the Lie algebra so(3,1)". United States.
doi:10.1070/SM2014v205n08ABEH004412.
```

```
@article{osti_22364911,
```

title = {Topological features of the Sokolov integrable case on the Lie algebra so(3,1)},

author = {Novikov, D V},

abstractNote = {The integrable Sokolov case on so(3,1){sup ⋆} is investigated. This is a Hamiltonian system with two degrees of freedom, in which the Hamiltonian and the additional integral are homogeneous polynomials of degrees 2 and 4, respectively. It is an interesting feature of this system that connected components of common level surfaces of the Hamiltonian and the additional integral turn out to be noncompact. The critical points of the moment map and their indices are found, the bifurcation diagram is constructed, and the topology of noncompact level surfaces is determined, that is, the closures of solutions of the Sokolov system on so(3,1) are described. Bibliography: 24 titles.},

doi = {10.1070/SM2014v205n08ABEH004412},

journal = {Sbornik. Mathematics},

number = 8,

volume = 205,

place = {United States},

year = {Sun Aug 31 00:00:00 EDT 2014},

month = {Sun Aug 31 00:00:00 EDT 2014}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.