Browsing by Author "Cima Mollet, Anna"

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 (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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 (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 ... 
Nonintegrability of measure preserving maps via Lie symmetries
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20151115)
Article
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 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 ... 
Parrondo's dynamic paradox for the stability of nonhyperbolic fixed points
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20170120)
Working paper
Open AccessWe show that for periodic nonautonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the ... 
Parrondo's dynamic paradox for the stability of nonhyperbolic fixed points
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (201802)
Article
Open AccessWe show that for periodic nonautonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for ... 
Periodic points, Lie symmetries and nonintegrability of planar maps
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (20170703)
Lecture
Open Access