Linearizability of the polynomial differential systems with a resonant singular point

Integrability and linearizability of polynomial differential systems are studied. The computation of generalized period constants is a way to find necessary conditions for linearizable systems for any rational resonance ratio. A method to compute generalized period constants is given. The algorithm is recursive and easy to realize with computer algebraic system. As the application, we discuss linearizable conditions for several Lotka–Volterra systems, and where this is the first time that the linearizability is considered for 3:−4 and 3:−5 resonances.