Painlevé Property and Integrability of Polynomial Dynamical Systems

Abstract

The main purpose of this paper is to investigate the connection between the Painlevé property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlevé property, then it admits certain class of first integrals. We also present some relationships between the Painlevé property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.