Painlevé Property and Integrability of Polynomial Dynamical Systems (Communications in Mathematical Research, 2021)
The main purpose of this paper is to investigate the connection betweenthe Painlevé property and the integrability of polynomial dynamical systems. Weshow that if a polynomial dynamical system has Painlevé property, then it admitscertain class of first integrals. We also present some relationships between the Painlevéproperty and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.