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

Volume 9, Issue 4, pp 1766--1775 http://dx.doi.org/10.22436/jnsa.009.04.32

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Authors

Yusen Wu - School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, Henan, P. R. China.

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.

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Keywords

• Generalized period constant
• recursive algorithm
• linearizability
• Lotka-Volterra system.

MSC

•  34C05
•  34C07

References

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