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Homogeneous-Like Generalized Cubic Systems

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  • G. R. Nicklason

Abstract

We consider properties and center conditions for plane polynomial systems of the forms , where , and , are polynomials of degrees and , respectively, for integers . We restrict our attention to those systems for which . In this case the system can be transformed to a trigonometric Abel equation which is similar in form to the one obtained for homogeneous systems . From this we show that any center condition of a homogeneous system for a given can be transformed to a center condition of the corresponding generalized cubic system and we use a similar idea to obtain center conditions for several other related systems. As in the case of the homogeneous system, these systems can also be transformed to Abel equations having rational coefficients and we briefly discuss an application of this to a particular Abel equation.

Suggested Citation

  • G. R. Nicklason, 2016. "Homogeneous-Like Generalized Cubic Systems," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-15, September.
    • Handle: RePEc:hin:jnijde:7640340
    DOI: 10.1155/2016/7640340
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