P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, TMF, 134:2 (2003), 207–226; Theoret. and Math. Phys., 134:2 (2003), 181

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 2, Pages 207–226
DOI: https://doi.org/10.4213/tmf154 (Mi tmf154)

This article is cited in 17 scientific papers (total in 17 papers)

Bifurcations of First Integrals in the Sokolov Case

P. E. Ryabov

Finance Academy under the Government of the Russian Federation

Full-text PDF (530 kB) Citations (17)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf154

Abstract: We study the phase topology of a new Liouville integrable Hamiltonian system with an additional quartic integral (the Sokolov case).

Keywords: Kirchhoff equations, integrable Hamiltonian systems, bifurcations of the Liouville tori.

Received: 20.02.2002

English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 2, Pages 181–197
DOI: https://doi.org/10.1023/A:1022224019967

Bibliographic databases:

Language: Russian

Citation: P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, TMF, 134:2 (2003), 207–226; Theoret. and Math. Phys., 134:2 (2003), 181–197

Citation in format AMSBIB

\Bibitem{Rya03}

\by P.~E.~Ryabov

\paper Bifurcations of First Integrals in the Sokolov Case

\jour TMF

\yr 2003

\vol 134

\issue 2

\pages 207--226

\mathnet{http://mi.mathnet.ru/tmf154}

\crossref{https://doi.org/10.4213/tmf154}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2025795}

\zmath{https://zbmath.org/?q=an:1178.37052}

\elib{https://elibrary.ru/item.asp?id=13423462}

\transl

\jour Theoret. and Math. Phys.

\yr 2003

\vol 134

\issue 2

\pages 181--197

\crossref{https://doi.org/10.1023/A:1022224019967}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000181522200004}

Linking options:

https://www.mathnet.ru/eng/tmf154

https://doi.org/10.4213/tmf154

https://www.mathnet.ru/eng/tmf/v134/i2/p207

This publication is cited in the following 17 articles:

V. A. Kibkalo, D. A. Tuniyants, “Uporyadochennye billiardnye igry i topologicheskie svoistva billiardnykh knizhek”, Trudy Voronezhskoi zimnei matematicheskoi shkoly S. G. Kreina — 2024, SMFN, 70, no. 4, Rossiiskii universitet druzhby narodov, M., 2024, 610–625
V. A. Kibkalo, “Parabolicity of degenerate singularities in axisymmetric Euler systems with a gyrostat”, Moscow University Mathematics Bulletin, 78:1 (2023), 28–36
Anatoly T. Fomenko, Vladislav A. Kibkalo, Understanding Complex Systems, Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, 2021, 3
Kibkalo V., “Topological Classification of Liouville Foliations For the Kovalevskaya Integrable Case on the Lie Algebra So(3,1)”, Topology Appl., 275 (2020), 107028
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
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
Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65
P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317
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
D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{so}(3,1)$ ”, Sb. Math., 205:8 (2014), 1107–1132
V. D. Irtegov, T. N. Titorenko, “Computer algebra methods in the study of nonlinear differential systems”, Comput. Math. Math. Phys., 53:6 (2013), 845–857
Valentin Irtegov, Tatyana Titorenko, Lecture Notes in Computer Science, 8136, Computer Algebra in Scientific Computing, 2013, 179
D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$ ”, Sb. Math., 202:5 (2011), 749–781
Irtegov V., Titorenko T., “On the peculiar properties of families of invariant manifolds of conservative systems”, Computer Algebra in Scientific Computing, Proceedings, Lecture Notes in Computer Science, 4770, 2007, 195–210
Valentin D. Irtegov, Tatyana N. Titorenko, “On One Approach to Investigation of Mechanical Systems”, SIGMA, 2 (2006), 049, 20 pp.
P. V. Morozov, “Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations”, Sb. Math., 195:3 (2004), 369–412
Fomenko A.T., Morozov P.V., “Some new results in topological classification of integrable systems in rigid body dynamics”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 201–222

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

Statistics & downloads:
Abstract page:	635
Full-text PDF :	273
References:	67
First page:	1

Registration to the website

Logotypes