Global centers of the generalized polynomial Lienard differential systems

The global centers started to be studied seriously at the end of the XX century. In the last decades, the generalized polynomial Lienard differential systems have been studied intensively. In this paper we characterize all the generalized polynomial Lienard differential systems having a global center at the origin. In particular we provide the explicit expressions of all the generalized polynomial Lienard differential systems of degree 3 having a global center at the origin, and the explicit expression of a generalized polynomial Lienard differential system of degree 5 having a global center at the origin.(c) 2022 Elsevier Inc. All rights reserved.