Calculation of generalized period constants via time-angle difference for complex analytic systems with resonant ratio

Abstract

In the case of a critical point being a center, the isochronicity problem (or linearizability problem) is far to be solved in general. A progressive way to find necessary conditions for isochronicity is to compute period constants. In this paper, we establish a new recursive algorithm of calculation of the so-called generalized period constants. Furthermore, we verify the new algorithm by the existing results for the Lotka-Volterra system with 3 : −2 resonance. Finally, the algorithm is applied to solve the linearizability problem for the Lotka-Volterra system in the ratio 4 : −5.