Almost exponential maps and integrability results for a class of horizontally regular vector fields

TL;DR

This paper establishes a higher order integrability theorem for certain vector fields with horizontal regularity, utilizing almost exponential maps as charts to analyze their structure.

Contribution

Introduces a higher order integrability theorem for horizontally regular vector fields using a novel class of almost exponential maps as charts.

Findings

Proves higher order integrability under horizontal regularity assumptions

Develops a detailed analysis of almost exponential maps

Provides new tools for studying vector fields with horizontal regularity

Abstract

We show a higher order integrability theorem for distributions generated by a family of vector fields under a horizontal regularity assumption on their coefficients. We use as chart a class of almost exponential maps which we discuss in details