RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 8, Pages 14–24 (Mi ivm9024)  

This article is cited in 1 scientific paper (total in 1 paper)

Application of normalized key functions in a problem of branching of periodic extremals

E. V. Derunova, Yu. I. Sapronov

Chair of Mathematical Modeling, Voronezh State University, 1 University sq., Voronezh, 394006 Russia

Abstract: In this paper we construct a procedure of approximate calculation and analysis of branches of bifurcating solutions to a periodic variational problem. The goal of the work is a study of bifurcation of cycles in dynamic systems in cases of double resonances $1:2:3$, $1:2:4$, $p:q:p+q$ and others. An ordinary differential equation (ODE) of the sixth order is considered as a general model equation. Application of the Lyapunov–Schmidt method and transition to boundary and angular singularities allow to simplify a description of branches of extremals and caustics. Also we list systems of generators of algebraic invariants under an orthogonal semi-free action of the circle on $\mathbb R^6$ and normal forms of the main part of the key functions.

Keywords: Fredholm functionals, extremals, circular symmetry, resonance, bifurcation, Lyapunov–Schmidt method.

Full text: PDF file (249 kB)
References: PDF file   HTML file

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:8, 9–18

Document Type: Article
UDC: 517.958
Received: 22.02.2014

Citation: E. V. Derunova, Yu. I. Sapronov, “Application of normalized key functions in a problem of branching of periodic extremals”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 8, 14–24; Russian Math. (Iz. VUZ), 59:8 (2015), 9–18

Citation in format AMSBIB
\Bibitem{DerSap15}
\by E.~V.~Derunova, Yu.~I.~Sapronov
\paper Application of normalized key functions in a~problem of branching of periodic extremals
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 8
\pages 14--24
\mathnet{http://mi.mathnet.ru/ivm9024}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 8
\pages 9--18
\crossref{https://doi.org/10.3103/S1066369X15080022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84937931032}


Linking options:
  • http://mi.mathnet.ru/eng/ivm9024
  • http://mi.mathnet.ru/eng/ivm/y2015/i8/p14

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. D. V. Kostin, “Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient”, Sb. Math., 207:12 (2016), 1709–1728  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Number of views:
    This page:104
    Full text:33
    References:22
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019