Nonlinear Stokes phenomena analytic classification invariants via generic perturbation
Abstract
For a generic deformation of a twodimensional holomorphic vector field with elementary degenerate singular point (saddlenode) we express the Martinet  Ramis orbital analytic classification invariants of the nonperturbed field in terms of the limit transitions between the linearizing charts of singularities of the perturbed field. In the case, when the multiplicity of the singular point of the nonperturbed field is equal to 2, we show that the Martinet  Ramis invariants are limits of transition functions that compare appropriately normalized canonic first integrals of the perturbed field in the linearizing charts. We prove a generalization of this statement for higher multiplicity singularities. For a generic deformation of higherdimensional holomorphic vector field with saddlenode singularity we show that appropriate sectorial central manifolds of the nonperturbed field are limits of appropriate separatrices of singularities of the perturbed field. We prove the analogues of the two first results for Ecalle  Voronin analytic classification invariants of onedimensional conformal maps tangent to identity.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1999
 arXiv:
 arXiv:math/9904151
 Bibcode:
 1999math......4151G
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Complex Variables;
 34C35;
 34A20
 EPrint:
 44 pages, 11 figures