(1 + d/dz)^(-1)
Algebraic Geometry
2016-10-04 v2 Analysis of PDEs
Classical Analysis and ODEs
Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1203.3045,
title = {(1 + d/dz)^(-1)},
author = {Michael McQuillan and Daniel Panazzolo},
journal= {arXiv preprint arXiv:1203.3045},
year = {2016}
}
Comments
This paper has been withdrawn due to an error in the proof of Claim I.3.5