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• Rational periodic sequences for the Lyness recurrence ﻿

(2010-04-30)
Altres
Accés obert
Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with ...
• The period function for Hamiltonian systems with homogeneous nonlinearities ﻿

(1996)
Article
Accés obert
The paper deals with Hamiltonian systems with homogeneous nonlinearities. We prove that such systems have no isochronous centers, that the period annulus of any of its centres is either bounded or the whole plane and that ...
• The period function for second-order quadratic ODEs is monotone ﻿

(2003)
Article
Accés obert
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 ...
• Upper bounds for the number of zeroes for some Abelian integrals ﻿

(2012-09)
Article
Accés restringit per política de l'editorial
Consider the vector field x′=−yG(x,y),y′=xG(x,y), where the set of critical points {G(x,y)=0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal directions. We perturb it ...
• Upper bounds for the number of zeroes for some Abelian Integrals ﻿

(2012-01-12)
Report de recerca
Accés obert
Abstract. Consider the vector field x0 = -yG(x, y), y0 = xG(x, y), where the set of critical points {G(x, y) = 0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal ...