Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities

摘要

In this paper we investigate the linearizability problem for the two-dimensional time-reversible complex system x = x + P(x, y), y = -y + Q(x, y), where P and Q are homogeneous quartic polynomials. The necessary and sufficient conditions for the linearizability of this system are found. As a corollary, the necessary and sufficient conditions for the origin to be an isochronous center of the planar time-reversible real system u = -v + F(u, v), v = u + G(u, v), where F and G are homogeneous quartic polynomials, are obtained.