Exponential map of germs of vector fields

TL;DR

This paper introduces an exponential map from germs of vector fields to germs of diffeomorphisms at zero, highlighting its non-bijective nature and reviewing related analytic iteration results.

Contribution

It presents a novel exponential map for germs of vector fields and analyzes its properties, expanding understanding of local diffeomorphism groups.

Findings

The exponential map is not a bijection.

Provides insights into the structure of germs of vector fields.

Reviews key results in analytic iteration theory.

Abstract

In this paper we introduce an exponential map of the algebra of germs of vector fields into the group of germs of diffeomorphisms at zero. It is shown that this mapping is not a bijection. A brief review of the key results of the analytic iteration problem is given.