Analytic classification of families of linear differential systems unfolding a resonant irregular singularity
Dynamical Systems
2020-01-24 v7 Classical Analysis and ODEs
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 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.
Keywords
Cite
@article{arxiv.1301.5228,
title = {Analytic classification of families of linear differential systems unfolding a resonant irregular singularity},
author = {Martin Klimeš},
journal= {arXiv preprint arXiv:1301.5228},
year = {2020}
}