First derivative of the period function with applications

Armengol Gasull; Emilio Freire; Antoni Guillamon

doi:https://doi.org/10.1016/j.jde.2004.04.005

First derivative of the period function with applications

Armengol Gasull, Emilio Freire, Antoni Guillamon

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

36 Citations (Scopus)

Abstract

Given a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study this function, and the use of commutators and Lie bracket was restricted to prove isochronicity. We give several examples and a special method which simplifies the computations when a first integral is known. © 2004 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	139-162
Journal	Journal of Differential Equations
Volume	204
DOIs	https://doi.org/10.1016/j.jde.2004.04.005
Publication status	Published - 10 Sep 2004

Keywords

Center
Lie symmetries
Period function
Planar system

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AU - Freire, Emilio

AU - Guillamon, Antoni

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N2 - Given a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study this function, and the use of commutators and Lie bracket was restricted to prove isochronicity. We give several examples and a special method which simplifies the computations when a first integral is known. © 2004 Elsevier Inc. All rights reserved.

AB - Given a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study this function, and the use of commutators and Lie bracket was restricted to prove isochronicity. We give several examples and a special method which simplifies the computations when a first integral is known. © 2004 Elsevier Inc. All rights reserved.

KW - Center

KW - Lie symmetries

KW - Period function

KW - Planar system

U2 - https://doi.org/10.1016/j.jde.2004.04.005

DO - https://doi.org/10.1016/j.jde.2004.04.005

M3 - Article

VL - 204

SP - 139

EP - 162

ER -