A note on the convergence of multivariate formal power series solutions of meromorphic Pfaffian systems

TL;DR

This paper extends existing theorems on the convergence of multivariate formal power series solutions for meromorphic Pfaffian systems, especially in cases involving non-integrability and degeneracy.

Contribution

It provides new insights into the convergence behavior of solutions in non-integrable and degenerate cases, complementing prior theorems focused on integrable systems.

Findings

Extended convergence results to non-integrable systems

Addressed cases with degenerate linear parts

Complemented classical theorems of Gerard and Sibuya

Abstract

Here we present some compliments to theorems of Gerard and Sibuya, on the convergence of multivariate formal power series solutions of nonlinear meromorphic Pfaffian systems. Their the most known results concern completely integrable systems with nondegenerate linear parts, whereas we consider some cases of non-integrability and degeneracy.