Critical point quantities and integrability conditions for a class of quintic systems

Abstract

For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given. The technique employed is essentially different from usual ones. The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations. Some results show an interesting contrast with the related results on quadratic systems.

Keywords

quintic system / critical point quantity / integrability condition / node quantity

References

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