RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

 Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 317–344 (Mi rcd46)

The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$

Abstract: In 2001, A.V. Borisov, I.S. Mamaev, and V.V. Sokolov discovered a new integrable case on the Lie algebra $so(4)$. This system coincides with the Poincaré equations on the Lie algebra $so(4)$, which describe the motion of a body with cavities filled with an incompressible vortex fluid. Moreover, the Poincaré equations describe the motion of a four-dimensional gyroscope. In this paper topological properties of this system are studied. In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, a classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.

Keywords: integrable Hamiltonian systems, isoenergy surfaces, Kirchhoff equations, Liouville foliation, bifurcation diagram, Borisov–Mamaev–Sokolov case, topological invariant

DOI: https://doi.org/10.1134/S1560354715030089

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J35, 70H06
Language:

Citation: Rasoul Akbarzadeh, Ghorbanali Haghighatdoost, “The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 20:3 (2015), 317–344

Citation in format AMSBIB
\Bibitem{AkbHag15} \by Rasoul Akbarzadeh, Ghorbanali Haghighatdoost \paper The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$ \jour Regul. Chaotic Dyn. \yr 2015 \vol 20 \issue 3 \pages 317--344 \mathnet{http://mi.mathnet.ru/rcd46} \crossref{https://doi.org/10.1134/S1560354715030089} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3357279} \zmath{https://zbmath.org/?q=an:06488660} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..317A} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000356354200008} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84934897371} 

• http://mi.mathnet.ru/eng/rcd46
• http://mi.mathnet.ru/eng/rcd/v20/i3/p317

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Rasoul Akbarzadeh, “Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 21:1 (2016), 1–17
2. Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592
3. A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525
4. P. E. Ryabov, “Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke”, Dokl. Math., 95:1 (2017), 17–20
5. R. Akbarzadeh, “The topology of isoenergetic surfaces for the Borisov–Mamaev–Sokolov integrable case on the Lie algebra $so(3,1)$”, Theoret. and Math. Phys., 197:3 (2018), 1727–1736