Abstract
This paper, using pseudo-division algorithm, introduces a method for computing resonant focus numbers of a class of complex polynomial differential systems, establishes the necessary and sufficient conditions for existence of a center for a class of complex quartic systems with a degenerate resonant singular point.
Highlights
In the qualitative theory of real planar differential systems, focal values and saddle values are two important detection quantities
In [2], the authors introduce a new efficient computational method, which combines the computation of focal values and saddle values into a unified calculation of singular point quantities for a class of complex planar differential systems
Using a perturbation technique based on multiple time scales, Yu [25] presents an efficient method for computing focal values of some classes of differential systems
Summary
In the qualitative theory of real planar differential systems, focal values and saddle values are two important detection quantities. Using pseudo-divisions, Wang [21] gives an improved formal power series method for computing focal values of a class of polynomial differential systems.
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