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






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


Nelin. Dinam., 2016, Volume 12, Number 3, Pages 413–541 (Mi nd535)  

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

Classic works. Historical pages

Monodromy of the fibre with oscillatory singular point of type $1:(-2)$

N. N. Nekhoroshev

Lomonosov Moscow State University, GSP-1, 1-52, Leninskie gory, 119991, Moscow, Russia

Abstract: In the present work, we prove the existence of fractional monodromy in a large class of compact Lagrangian fibrations of four-dimensional symplectic manifolds. These fibrations are considered in the neighbourhood of the singular fibre $\lambda_0$, that has a single singular point corresponding to a nonlinear oscillator with frequencies in $1:(-2)$ resonance. We compute the matrices of monodromy defined by going around the fibre $\lambda_0$. For all fibrations in the class and for an appropriate choice of the basis in the one-dimensional homology group of the torus, these matrices are the same. The elements of the monodromy matrix are rational and there is a non-integer element among them. This work is a continuation of the analysis in [20, 21, 39] where the matrix of fractional monodromy was computed for most simple particular fibrations of the class.

DOI: https://doi.org/10.20537/nd1603008

Full text: PDF file (1366 kB)
References: PDF file   HTML file

UDC: 517.93+514.745.82
MSC: 37J35, 58K10

Citation: N. N. Nekhoroshev, “Monodromy of the fibre with oscillatory singular point of type $1:(-2)$”, Nelin. Dinam., 12:3 (2016), 413–541

Citation in format AMSBIB
\Bibitem{Nek16}
\by N.~N.~Nekhoroshev
\paper Monodromy of the fibre with oscillatory singular point of type $1:(-2)$
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 3
\pages 413--541
\mathnet{http://mi.mathnet.ru/nd535}
\crossref{https://doi.org/10.20537/nd1603008}
\elib{http://elibrary.ru/item.asp?id=27328722}


Linking options:
  • http://mi.mathnet.ru/eng/nd535
  • http://mi.mathnet.ru/eng/nd/v12/i3/p413

    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
    Addendum

    This publication is cited in the following articles:
    1. Dmitrií A. Sadovskií, “Nekhoroshev’s Approach to Hamiltonian Monodromy”, Regul. Chaotic Dyn., 21:6 (2016), 720–758  mathnet  crossref  mathscinet
  • Нелинейная динамика
    Number of views:
    This page:139
    Full text:39
    References:20

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