We prove a formula for the $n$-th derivative of the period function $T$ in a
period annulus of a planar differential system. For $n = 1$, we obtain Freire,
Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We
apply such a result to hamiltonian systems with separable variables and other
systems. We give some sufficient conditions for the period function of
conservative second order O.D.E.'s to be convex.Comment: 2 figure

Sabatini, Marco

English

arXiv

We prove a formula for the n-th derivative of the period function T in a period annulus of a planar differential system. For n = 1, we obtain Freire, Gasull and Guillamon formula for the period’s first derivative [17]. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order O.D.E.’s to be convex

M. Sabatini

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The period functions ’ higher order derivatives

We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order O.D.E.'s to be convex

The period functions' higher order derivatives

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