Browsing by Author "Gasull Embid, Armengol"

Integrability and nonintegrability of periodic nonautonomous Lyness recurrences
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20131201)
Article
Open AccessThis paper studies nonautonomous Lynesstype recurrences of the form x n+2 = (a n + x n+1)/x n , where {a n } is a kperiodic sequence of positive numbers with primitive period k. We show that for the cases k {1, 2, 3, ... 
Integrability and nonintegrability of periodic nonautonomous Lyness recurrences
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20101222)
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Open AccessThis paper studies nonautonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a kperiodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the ... 
Integrability and nonintegrability of periodic nonautonomous Lyness recurrences (revised and enlarged version)
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20111222)
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Open AccessThis paper studies nonautonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a kperiodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the ... 
Limit cycles and Lie symmetries
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2005)
Article
Open AccessGiven 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
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2005)
Article
Open AccessThis paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of onedimensional nonautonomous differential equations: those with the righthand sides being polynomials of ... 
Non autonomous 2periodic GumovskiMira difference equations
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20110601)
External research report
Open AccessWe consider two types of nonautonomous 2periodic GumovskiMira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2periodic ... 
Nonautonomous two periodic GumovskiMira difference equations
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (201212)
Article
Open AccessWe consider two types of nonautonomous twoperiodic Gumovski–Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the twoperiodic ... 
Nonintegrability of measure preserving maps via Lie symmetries
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20151115)
Article
Restricted access  publisher's policyWe consider the problem of characterizing, for certain natural number m, the local C^mnonintegrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this nonintegrability ... 
Nonintegrability of measure preserving maps via Lie symmetries
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20150318)
External research report
Open AccessWe consider the problem of characterizing, for certain natural number m, the local C^mnonintegrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this nonintegrability ... 
On 2 and 3periodic Lyness difference equations
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20110609)
Article
Open AccessWe describe the sequences {xn}n given by the nonautonomous secondorder Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2periodic or a 3 periodic sequence of positive values and the initial ... 
On Poncelet's maps
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20100808)
Article
Open AccessGiven 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 ... 
On the Chebyshev property for a new family of functions
Lázaro Ochoa, José Tomás; Gasull Embid, Armengol; Torregrosa, Joan (201203)
Article
Open Access 
On two and three periodic Lyness difference equations
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20091226)
External research report
Open AccessWe describe the sequences {x_n}_n given by the nonautonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2periodic or a 3periodic sequence of positive values and the ... 
Period function for perturbed isochronous centres
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2001)
Article
Open Access 
Phase portrait of Hamiltonian systems with homogeneous nonlinearities
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1999)
Article
Open AccessThe 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
Gasull Embid, Armengol; Mañosa Fernández, Víctor; Xarles Ribas, Xavier (20100430)
Other
Open AccessConsider 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
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor; Mañosas Capellades, Francesc (1996)
Article
Open AccessThe 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 secondorder quadratic ODEs is monotone
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Villadelprat Yagüe, Jordi (2003)
Article
Open AccessVery 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 secondorder diﬀerential ... 
Upper bounds for the number of zeroes for some Abelian integrals
Gasull Embid, Armengol; Lázaro Ochoa, José Tomás; Torregrosa, Joan (201209)
Article
Restricted access  publisher's policyConsider 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
Lázaro Ochoa, José Tomás; Gasull Embid, Armengol; Torregrosa, Joan (20120112)
External research report
Open AccessAbstract. 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 ...