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arXiv · 1301.5228

Analytic classification of families of linear differential systems unfolding a resonant irregular singularity

Martin Klimeš
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Abstract

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 Poincare 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 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.

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Martin Klimeš. 2013-01-22. Analytic classification of families of linear differential systems unfolding a resonant irregular singularity. https://doi.org/10.3842/sigma.2020.006

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