Abstract
In this paper we present the necessary and sufficient conditions for linearizability of the planar time-reversible cubic complex system x ˙ = x + P ( x , y ) , y ˙ = − y + Q ( x , y ) . From these conditions, the necessary and sufficient conditions for the origin to be an isochronous center of the time-reversible cubic real system u ˙ = − v + F ( u , v ) , v ˙ = u + G ( u , v ) can be obtained. Thus, the isochronous center problem of time-reversible cubic systems is solved completely.
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