The period functions' higher order derivatives

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 (Unpublished)

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    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
    Department or Research center: Mathematics
    Subjects: Q Science > QA Mathematics > QA299.6 Analysis
    Uncontrolled Keywords: Period annulus, period function, normalizer, linearization, hamiltonian system, separable variables.
    Report Number: UTM 750
    Repository staff approval on: 23 Feb 2012

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