On a maximal number of period annuli. (English) Zbl 1210.34046

Summary: We consider the equation \(x''+g(x) = 0\), where \(g(x)\) is a polynomial, allowing the equation to have multiple period annuli. We detect the maximal number of possible period annuli for polynomials of odd degree and show how the respective optimal polynomials can be constructed.


34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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