## Geometrical aspects of stability theory for Hill’s equations.(English)Zbl 0840.34047

For the equation $$x''+ (a+ bp(t)) x= 0$$, $$p(t)\equiv p(t+ 2\pi)$$ ($$a$$, $$b$$ are real parameters) the authors introduce the Hill’s map by $$H: (a, b)\mapsto P_{a, b}$$, where $$P_{a, b}$$ is the Poincaré (or period) matrix of the equation. They give a global geometric picture of this map, which explains the nature of the classical stability domains in the parameter plane.
Reviewer: L.Hatvani (Szeged)

### MSC:

 34D05 Asymptotic properties of solutions to ordinary differential equations 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 70J40 Parametric resonances in linear vibration theory
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### References:

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