Linearizability of homogeneous quartic polynomial systems with 1:−2 resonance

Abstract

a b s t r a c tIn this paper, we consider the linearizability problem of complex planar polynomial systems of the formẋ = x + P 4 ,ẏ = −2y − Q 4 , where P 4 and Q 4 are homogeneous quartic polynomials. We obtain the necessary and sufficient conditions for linearizing the systems.