### Enviaments recents

• #### Continua of periodic points for planar integrable rational maps. ﻿

(2015-11-30)
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We 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 ...
• #### Desigualtats matricials lineals amb valors complexos ﻿

(2015-07-12)
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Sovint ens trobem davant de desigualtats matricials lineals (LMIs) on les matrius involucrades prenen valors complexos. Es ben conegut que tota LMI complexa es pot reduir a una LMI real. En aquest treball establim les ...
• #### Non-integrability of measure preserving maps via Lie symmetries ﻿

(2015-03-18)
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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 ...
• #### Singular solutions for a class of traveling wave equations arising in hydrodynamics ﻿

(2015-02-19)
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We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form $\ddot{u}\,u + \frac{1}{2}\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function. Our motivation stems ...
• #### Lie symmetries of birational maps preserving genus 0 fibrations ﻿

(2015-02-13)
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We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic ...
• #### Periodic orbits of planar integrable birational maps ﻿

(2014-02-14)
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A birational planar map F possessing a rational ﬁrst integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically ...
• #### Basin of attraction of triangular maps with applications ﻿

(2013-07-25)
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We 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 ...
• #### Different approaches to the global periodicity problem ﻿

(2013-07-25)
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t Let F be a real or complex n-dimensional 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 ...
• #### On the set of periods of the 2-periodic Lyness’ Equation ﻿

(2013-07-25)
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We study the periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)=un, where fangn is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues ...
• #### Periodic orbits of planar integrable birational maps ﻿

(2013-09-03)
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