Integrability and linearizability of cubic Z2 systems with non-resonant singular points

Abstract

In this paper, complete integrability and linearizability of cubic Z2 systems with two non-resonant and elementary singular points are investigated. First of all, four simple normal forms are obtained based on the coefficients and eigenvalues of cubic Z2 systems. Then, the integrable and linearizable conditions are classified according to the four different cases respectively, and the problem is solved thoroughly for cubic Z2 systems with two non-resonant singular points.