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Moscow Mathematical Journal, 2012, Volume 12, Number 1, Pages 77–138
DOI: https://doi.org/10.17323/1609-4514-2012-12-1-77-138
(Mi mmj449)
 

This article is cited in 16 scientific papers (total in 16 papers)

Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1

Caroline Lambert, Christiane Rousseau

Département de Mathématiques et de Statistique, Université de Montréal, Montréal (Qc), Canada
Full-text PDF Citations (16)
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Abstract: In this, paper, we give a complete system of analytic invariants for the unfoldings of nonresonant linear differential systems with an irregular singularity of Poincarй rank 1 at the origin over a fixed neighborhood $\mathbb D_r$. The unfolding parameter $\epsilon$ is taken in a sector $S$ pointed at the origin of opening larger than $2\pi$ in the complex plane, thus covering a whole neighborhood of the origin. For each parameter value $\epsilon\in S$, we cover $\mathbb D_r$ with two sectors and, over each sector, we construct a well chosen basis of solutions of the unfolded linear differential systems. This basis is used to find the analytic invariants linked to the monodromy of the chosen basis around the singular points. The analytic invariants give a complete geometric interpretation to the well-known Stokes matrices at $\epsilon=0$: this includes the link (existing at least for the generic cases) between the divergence of the solutions at $\epsilon=0$ and the presence of logarithmic terms in the solutions for resonance values of the unfolding parameter. Finally, we give a realization theorem for a given complete system of analytic invariants satisfying a necessary and sufficient condition, thus identifying the set of modules.
Key words and phrases: Stokes phenomenon, irregular singularity, unfolding, confluence, divergent series, monodromy, Riccati matrix differential equation, analytic classification, summability, realization.
Received: August 24, 2010; in revised form May 5, 2011
Bibliographic databases:
Document Type: Article
MSC: Primary 34M35, 34M40, 34M50, 34M03; Secondary 37G10, 34E10, 37G05
Language: English
Citation: Caroline Lambert, Christiane Rousseau, “Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1”, Mosc. Math. J., 12:1 (2012), 77–138
Citation in format AMSBIB
\Bibitem{LamRou12}
\by Caroline Lambert, Christiane Rousseau
\paper Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincar\'e rank~1
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 77--138
\mathnet{http://mi.mathnet.ru/mmj449}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-77-138}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2952427}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000309364900006}
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  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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