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

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

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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} 

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

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