On the nonlinear Poincaré flow

Abstract

We develop a tool in order to analyse the dynamics of differentiable flows with singularities. It provides an abstract model for the local dynamics that can be used in order to control the size of invariant manifolds. This work is the first part of the results announced in [CY2].

We thought our previous text arXiv:1702.05994 was too long and decided to split it. This one is the first part. We have added comments and improved the presentation