RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find






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


Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 163, Pages 65–80 (Mi into451)  

Parametric resonance in integrable systems and averaging on Riemann surfaces

V. Yu. Novokshenov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

Abstract: In this paper, we consider adiabatic deformations of Riemann surfaces that preserve the integrability of the corresponding dynamic system, which leads to the appearance of modulated quasi-periodic motions, similar to the effect of parametric resonance. We show that in this way it is possible to control the amplitude and frequency of nonlinear modes. We consider several examples of the dynamics of top-type systems.

Keywords: integrable system, Lax pair, algebraic-geometric method, finite-gap solution, theta function, invariant torus, parametric resonance, Whitham deformation, synchronization, phase capture

Full text: PDF file (356 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 517.928, 517.933, 517.984.54
MSC: 37J35, 37K15, 37K20

Citation: V. Yu. Novokshenov, “Parametric resonance in integrable systems and averaging on Riemann surfaces”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 65–80

Citation in format AMSBIB
\Bibitem{Nov19}
\by V.~Yu.~Novokshenov
\paper Parametric resonance in integrable systems and averaging on Riemann surfaces
\inbook Differential Equations
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 163
\pages 65--80
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into451}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4014976}


Linking options:
  • http://mi.mathnet.ru/eng/into451
  • http://mi.mathnet.ru/eng/into/v163/p65

    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
  • Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory" Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
    Number of views:
    This page:50
    Full text:20
    References:6
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020