### Recent Submissions

• #### Enquesta sobre la situació del col·lectiu del professorat associat a la Universitat Politècnica de Catalunya ﻿

(2021-03-15)
Research report
Open Access
La utilització de la figura del professorat associat per part de les universitats públiques a Catalunya en molts casos està lluny de l’esperit d’aquesta figura en la legislació (especialista de reconeguda competència i amb ...
• #### Persistence of periodic traveling waves and Abelian integrals ﻿

(2021-03-10)
Research report
Open Access
It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain ...
• #### Pointwise periodic maps with quantized first integrals ﻿

(2020-10-24)
Research report
Open Access
In a series of papers, Chang, Cheng and Wang studied the periodic behavior of some piecewise linear maps in the plane. These examples are valuable under the light of the classical result of Montgomery about periodic ...
• #### Periodic points of a Landen transformation ﻿

(2018-01-12)
Research report
Open Access
We prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced ...
• #### Bifurcation of 2-periodic orbits from non-hyperbolic fixed points ﻿

(2017-07-21)
Research report
Open Access
We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful ...
• #### Continua of periodic points for planar integrable rational maps. ﻿

(2015-11-30)
Research report
Open Access
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)
Research report
Open Access
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)
Research report
Open Access
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)
Research report
Open Access
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)
Research report
Open Access
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)
Research report
Open Access
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)
Research report
Open Access
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 ...