Browsing by Author "Gasull Embid, Armengol"

First derivative of the period function with applications
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2001)
Article
Open AccessGiven a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study ... 
Global periodicity conditions for maps and recurrences via Normal Forms
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20120504)
Other
Open AccessWe face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions ... 
Global periodicity conditions for maps and recurrences via normal forms
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (201311)
Article
Open AccessWe face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of K, where K is ℝ or ℂ, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary ... 
Identification of oneparameter bifurcations giving rise to periodic orbits, from their period function.
Gasull Embid, Armengol; Mañosa Fernández, Víctor; Villadelprat Yagüe, Jordi (Universitat Politècnica de Catalunya. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), 2009)
Conference report
Open Access 
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
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 (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 ...