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. © 2012 Elsevier Inc. All rights reserved.
The period functions' higher order derivatives / Sabatini, Marco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 253:10(2012), pp. 2825-2845. [10.1016/j.jde.2012.07.013]
The period functions' higher order derivatives
Sabatini, Marco
2012-01-01
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. © 2012 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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