(1 + d/dz)^(-1)

Details (1 + d/dz)^(-1) (1 + d/dz)^(-1)

2012-03-14

arxiv.org/abs/1203.3045v1

Mathematics

Algebraic Geometry

Scientific paper

We investigate the structure of fully non-linear P.D.E.'s in holomorphic functions, with emphasis on the functorial generalisation of so called "irregular" O.D.E.'s. Highlights are an implicit function theorem removing the perturbation conditions of Nash-Moser type, best possible existence results when the singularity of the linearised P.D.E. is at worst bi-dimensional, and various, again optimal, corollaries on existence of centre manifolds and conjugation to normal form of 3-dimensional vector fields.

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