# The period functions' higher order derivatives

Sabatini, Marco (2012) The period functions' higher order derivatives. UNSPECIFIED. (Unpublished)

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## Abstract

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.

Item Type: Departmental Technical Report Mathematics Q Science > QA Mathematics > QA299.6 Analysis Period annulus, period function, normalizer, linearization, hamiltonian system, separable variables. UTM 750 23 Feb 2012

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