Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities (Q938715)

This paper gives necessary and sufficient conditions that a polynomial system \[ \dot x = x + P(x,y), \qquad \dot y = -y + Q(x,y) \] on \(\mathbb{C}^2\) that is time-reversible be linearizable, in the case that the nonlinear terms are homogeneous quartic polynomials in \(x\) and \(y\). The author's method is to compute an initial string of the so-called linearizability quantities, find the irreducible decomposition of the complex variety that they generate, and then show that a system corresponding to an element of each component in a component is linearizable, typically using the method of Darboux linearization. Based on these results the authors also characterize when centers of corresponding real systems are isochronous.