Analytic integrability around a nilpotent singularity

TL;DR

This paper addresses the problem of determining when a planar differential system with a nilpotent singularity is analytically integrable, providing solutions under generic conditions.

Contribution

It offers a solution to the analytic integrability problem around nilpotent singularities in planar systems under generic conditions, advancing the understanding of such singularities.

Findings

Provides criteria for analytic integrability near nilpotent singularities

Establishes generic conditions for integrability

Advances theoretical understanding of nilpotent singularities

Abstract

In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.