Now showing items 16-32 of 32

• #### Limit cycles and Lie symmetries ﻿

(2005)
Article
Open Access
Given a planar vector ﬁeld U which generates the Lie symmetry of some other vector ﬁeld X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem ...
• #### Limit cycles for generalized Abel equations ﻿

(2005)
Article
Open Access
This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional non-autonomous differential equations: those with the right-hand sides being polynomials of ...
• #### Non autonomous 2-periodic Gumovski-Mira difference equations ﻿

(2011-06-01)
External research report
Open Access
We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ...
• #### Non-autonomous two periodic Gumovski-Mira difference equations ﻿

(2012-12)
Article
Open Access
We consider two types of nonautonomous two-periodic Gumovski–Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the two-periodic ...
• #### Non-integrability of measure preserving maps via Lie symmetries ﻿

(2015-11-15)
Article
Restricted access - publisher's policy
We consider the problem of characterizing, for certain natural number m, the local C^m-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability ...
• #### Non-integrability of measure preserving maps via Lie symmetries ﻿

(2015-03-18)
External research report
Open Access
We consider the problem of characterizing, for certain natural number m, the local C^m-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability ...
• #### On 2- and 3-periodic Lyness difference equations ﻿

(2011-06-09)
Article
Open Access
We describe the sequences {xn}n given by the non-autonomous second-order Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2-periodic or a 3- periodic sequence of positive values and the initial ...
• #### On Poncelet's maps ﻿

(2010-08-08)
Article
Open Access
Given two ellipses, one surrounding the other one, Poncelet introduced a map P from the exterior one to itself by using the tangent lines to the interior ellipse. This procedure can be extended to any two smooth, nested ...

(2012-03)
Article
Open Access
• #### On two and three periodic Lyness difference equations ﻿

(2009-12-26)
External research report
Open Access
We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the ...

(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 ...