dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor
Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author
Gasull Embid, Armengol
dc.contributor.author
Guillamon Grabolosa, Antoni
dc.contributor.author
Villadelprat Yagüe, Jordi
dc.identifier
https://hdl.handle.net/2117/847
dc.description.abstract
Very 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.format
application/pdf
dc.rights
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.rights
Attribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject
Differential equations
dc.subject
Differentiable dynamical systems
dc.subject
period function
dc.subject
Equacions diferencials ordinàries
dc.subject
Sistemes dinàmics diferenciables
dc.subject
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.title
The period function for second-order quadratic ODEs is monotone
