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

 Nelin. Dinam.: Year: Volume: Issue: Page: Find

 Nelin. Dinam., 2010, Volume 6, Number 4, Pages 769–805 (Mi nd5)

Topological analysis and Boolean functions. I. Methods and application to classical systems

M. P. Kharlamov

Abstract: We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as rational functions (in fact, as polynomials) in some set of radicals depending on one variable each. We suggest a method to define the admissible regions in the integral constants space, the segments of oscillation of the separated variables and the number of connected components of integral manifolds and critical integral surfaces. This method is based on some algorithms of processing the tables of some Boolean vector-functions and of reducing the matrices of linear Boolean vector-functions to some canonical form. From this point of view we consider here the topologically richest classical problems of the rigid body dynamics. The article will be continued with the investigation of some new integrable problems.

Keywords: algebraic separation of variables, integral manifolds, Boolean functions, topological analysis, algorithms.

Full text: PDF file (619 kB)
References: PDF file   HTML file
UDC: 517.938.5:531.38+519.6
MSC: 70E17, 70G40

Citation: M. P. Kharlamov, “Topological analysis and Boolean functions. I. Methods and application to classical systems”, Nelin. Dinam., 6:4 (2010), 769–805

Citation in format AMSBIB
\Bibitem{Kha10} \by M.~P.~Kharlamov \paper Topological analysis and Boolean functions. I.~Methods and application to classical systems \jour Nelin. Dinam. \yr 2010 \vol 6 \issue 4 \pages 769--805 \mathnet{http://mi.mathnet.ru/nd5} 

• http://mi.mathnet.ru/eng/nd5
• http://mi.mathnet.ru/eng/nd/v6/i4/p769

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
Cycle of papers

This publication is cited in the following articles:
1. Kharlamov M.P., Savushkin A.Yu., “Geometricheskii podkhod k razdeleniyu peremennykh v mekhanicheskikh sistemakh”, Vestn. Volgogradskogo gos. un-ta. Ser. 1: Matem. Fiz., 2010, no. 13, 47–74
2. M. P. Kharlamov, “Topologicheskii analiz i bulevy funktsii: II. Prilozheniya k novym algebraicheskim resheniyam”, Nelineinaya dinam., 7:1 (2011), 25–51
3. Ryabov P.E., “Explicit integration and topology of D. N. Goryachev case”, Dokl. Math., 84:1 (2011), 502–505
4. S. S. Nikolaenko, “The number of connected components in the preimage of a regular value of the momentum mapping for the geodesic flow on ellipsoid”, Moscow University Mathematics Bulletin, 68:5 (2013), 241–245
5. S. S. Nikolaenko, “A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid”, Sb. Math., 205:2 (2014), 224–268
6. P. E. Ryabov, “The phase topology of a special case of Goryachev integrability in rigid body dynamics”, Sb. Math., 205:7 (2014), 1024–1044
7. S. S. Nikolaenko, “Topological classification of the Goryachev integrable case in rigid body dynamics”, Sb. Math., 207:1 (2016), 113–139
8. Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65
9. Nikolaenko S.S., “Topological Classification of the Goryachev Integrable Systems in the Rigid Body Dynamics: Non-Compact Case”, Lobachevskii J. Math., 38:6 (2017), 1050–1060
10. I. F. Kobtsev, “Geodesic flow of a 2D ellipsoid in an elastic stress field: topological classification of solutions”, Moscow University Mathematics Bulletin, 73:2 (2018), 64–70
•  Number of views: This page: 247 Full text: 65 References: 38 First page: 1