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dc.contributor.authorGasull Embid, Armengol
dc.contributor.authorGuillamon Grabolosa, Antoni
dc.contributor.authorVilladelprat Yagüe, Jordi
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractVery little is known about the period function for large families of centers. In one of the pioneering works on this problem, Chicone [?] conjectured that all the centers encountered in the family of second-order differential equations ¨x = V (x, ˙ x), being V a quadratic polynomial, should have a monotone period function. Chicone solved some of the cases but some others remain still unsolved. In this paper we fill up these gaps by using a new technique based on the existence of Lie symmetries and presented in [?]. This technique can be used as well to reprove all the cases that were already solved, providing in this way a compact proof for all the quadratic second-order differential equations. We also prove that this property on the period function is no longer true when V is a polynomial which nonlinear part is homogeneous of degree n > 2.
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshDifferential equations
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherperiod function
dc.titleThe period function for second-order quadratic ODEs is monotone
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.rights.accessOpen Access

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Attribution-NonCommercial-NoDerivs 2.5 Spain
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