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

Symmetry Integrability and Geometry-Methods and Applications

article

Martin KLIMESˇ¹ 

[1] Independent Researcher

关键词: linear differential equations;    confluence of singularities;    Stokes phenomenon;    monodromy;    analytic classification;    moduli space;    biconfluent hypergeometric equation;   

DOI  :  10.3842/SIGMA.2020.006

来源: National Academy of Science of Ukraine

【 摘 要 】

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 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.

【 授权许可】

Unknown