Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity

We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincaré rank 1 in dimension n=2 whose leading matrix is a Jordan bloc. The moduli space of analytic equivalence c...

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Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2020
Main Author: Klimeš, Martin
Format: Article
Language:English
Published: Інститут математики НАН України 2020
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210604
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity. Martin Klimeš. SIGMA 16 (2020), 006, 46 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincaré rank 1 in dimension n=2 whose leading matrix is a Jordan bloc. The moduli space of analytic equivalence classes is described in terms of a tuple of formal invariants and a single analytic invariant obtained from the trace of monodromy, and analytic normal forms are given. We also explain the underlying phenomena of the confluence of two simple singularities and of a turning point, the associated Stokes geometry, and the change of order of Borel summability of formal solutions in dependence on a complex parameter.
ISSN:1815-0659