Now showing items 26-32 of 32

(2001)
Article
Open Access
• #### Phase portrait of Hamiltonian systems with homogeneous nonlinearities ﻿

(1999)
Article
Open Access
The main goal of this work is to describe the phase portarit of Hamiltonian systems with a non degenerate center at the origin and homogeneous nonlinearities of arbitrary degree n. We apply our results to the case n=2 to ...
• #### Rational periodic sequences for the Lyness recurrence ﻿

(2010-04-30)
Other
Open Access
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
Open Access
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
Open Access
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
Restricted access - publisher's policy
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)
External research report
Open Access
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 ...