Polynomial Differential Equations with Small coefficients

Details Polynomial Differential Equations with Small coefficients Polynomial Differential Equations with Small coefficients

2009-04-17

arxiv.org/abs/0904.2756v1

Mathematics

Classical Analysis and ODEs

15 pages

Scientific paper

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of the classes the upper bound can be improved when we consider real periodic solutions. We present a proof to a recent conjecture on the number of periodic solutions. The results are used to give upper bounds for the number of limit cycles of polynomial two-dimensional systems.

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