Browsing by Author "Gasull Embid, Armengol"

A characterization of isochronous centres in terms of symmetries
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2000)
Article
Open AccessWe present a description of isochronous centres of planar vector fields $X$ by means of their groups of symmetries. More precisely, given a normalizer $U$ of $X$ (i.e., $[X,U]=\mu X$, where $\mu$ is a scalar function), we ... 
An analyticnumerical method of computation of the Liapunov and period constants derived from their algebraic structure
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1996)
Article
Open AccessWe consider the problem of computing the Liapunov and the period constants for a smooth differential equation with a non degenerate critical point. First, we investigate the structure of both constants when they are ... 
An explicit expression of the first Liapunov and period constants with applications
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1996)
Article
Open AccessIn this paper, we study systems in the plane having a critical point with pure imaginary eigenvalues, and we search for effective conditions to discern whether this critical point is a focus or a center; in the case of it ... 
Basin of attraction of triangular maps with applications
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20130725)
External research report
Open AccessWe consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction ... 
Basin of attraction of triangular maps with applications
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (201403)
Article
Open AccessWe consider planar triangular maps that preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of ... 
Bifurcation of 2periodic orbits from nonhyperbolic fixed points
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (201801)
Article
Open AccessWe introduce the concept of 2cyclicity for families of onedimensional maps with a nonhyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful ... 
Bifurcation of 2periodic orbits from nonhyperbolic fixed points
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20170721)
External research report
Open AccessWe introduce the concept of 2cyclicity for families of onedimensional maps with a nonhyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful ... 
Centre and isochronicity conditions for systems with homogeneous nonlinearities
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1995)
Article
Open AccessWe study the centrefocus problem for systems with homogeneous nonlinearities. In the centre case we study the characterization of the isochronous centres. More explicitly, we derive six necessary conditions to be a ... 
Continua of periodic points for planar integrable rational maps
Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor (Research India Publications, 201609)
Article
Open AccessWe present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used by other authors and apply ... 
Continua of periodic points for planar integrable rational maps.
Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor (20151130)
External research report
Open AccessWe present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used for other authors and apply ... 
Different approaches to the global periodicity problem
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor; Mañosas, Francesc (20130725)
External research report
Open Accesst Let F be a real or complex ndimensional map. It is said that F is globally periodic if there exists some p ∈ N + such that Fp(x) = x for all x, where F k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is ... 
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 (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)
Other
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)
Other
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 ...