First derivative of the period function with applications

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 i...

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Bibliographic Details
Authors: Freire, Emilio, Gasull Embid, Armengol, Guillamon Grabolosa, Antoni|||0000-0001-8268-4503
Format: article
Publication Date:2001
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/818
Online Access:https://hdl.handle.net/2117/818
Access Level:Open access
Keyword:Differential equations
period function
Equacions diferencials ordinàries
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Description
Summary: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.