26 citations · 200 across the 32 of their papers we have counts for
32 papers
Dynamics of Kahan-Hirota-Kimura maps with rational invariant fibrations
Víctor Mañosa, Chara Pantazi
We present a simple method to study the dynamics of planar Kahan-Hirota-Kimura (KHK) maps preserving rational fibrations. Using this approach, we show that integrable KHK maps may…
Monodromic singularities of Brunella-Miari vector fields with two edges in the Newton diagram
Isaac A. García, Jaume Giné, Víctor Mañosa
This work focuses on the study of monodromic singularities in planar analytic families of vector fields whose Newton diagram consists of exactly two edges. We begin by analyzing th…
Entropy and ω-limit sets on invariant graphs for a class of planar piecewise linear maps
Anna Cima, Armengol Gasull, Víctor Mañosa +1
We consider the family of piecewise linear maps where . In previous work, we identified that certain maps of…
Invariant graphs and dynamics of a family of continuous piecewise linear planar maps
Anna Cima, Armengol Gasull, Víctor Mañosa +1
We consider the family of piecewise linear maps where . This family belongs to a wider one that has d…
On some rational piecewise linear rotations
Anna Cima, Armengol Gasull, Víctor Mañosa +1
We study the dynamics of the piecewise planar rotations with $z\in\C$, if if and $λ=\mathrm{e}^{i…
On the accumulation points of non-periodic orbits of a difference equation of fourth order
Antonio Linero Bas, Víctor Mañosa, Daniel Nieves Roldán
In this paper, we are interested in analyzing the dynamics of the fourth-order difference equation , with arbitrary real initial co…
Persistence of periodic traveling waves and Abelian integrals
Armengol Gasull, Anna Geyer, Víctor Mañosa
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…
Pointwise periodic maps with quantized first integrals
Anna Cima, Armengol Gasull, Víctor Mañosa +1
We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first inte…
A dynamic Parrondo's paradox for continuous seasonal systems
Anna Cima, Armengol Gasull, Víctor Mañosa
We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo's dynamic paradox, in which the stability of…
Phase portraits of random planar homogeneous vector fields
Anna Cima, Armengol Gasull, Víctor Mañosa
We study the phase portraits with positive probability of random planar homogeneous vector fields of degree n. In particular, for n=1,2,3, we give a complete solution of the proble…
Stability index of linear random dynamical systems
Anna Cima, Armengol Gasull, Víctor Mañosa
Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for th…
Minor loops of the Dahl and LuGre models
Fayçal Ikhouane, Víctor Mañosa, Gisela Pujol
Hysteresis is a special type of behavior encountered in physical systems: in a hysteretic system, when the input is periodic and varies slowly, the steady-state part of the output-…
Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem
Armengol Gasull, Víctor Mañosa
We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this…
A route to chaos in the Boros-Moll map
Laura Gardini, Víctor Mañosa, Iryna Sushko
The Boros-Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to the convergence of them. In the paper,…
Periodic points of a Landen transformation
Armengol Gasull, Mireia Llorens, Víctor Mañosa
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 o…
Bifurcation of 2-periodic orbits from non-hyperbolic fixed points
Anna Cima, Armengol Gasull, Víctor Mañosa
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…
Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points
Anna Cima, Armengol Gasull, Víctor Mañosa
We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed…
Non-integrability of measure preserving maps via Lie symmetries
Anna Cima, Armengol Gasull, Víctor Mañosa
We consider the problem of characterizing, for certain natural number , the local -non-integrability near elliptic fixed points of smooth planar measure preservin…
Singular solutions for a class of traveling wave equations arising in hydrodynamics
Anna Geyer, Víctor Mañosa
We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form , where is an a…
Lie Symmetries of Birational Maps Preserving Genus 0 Fibrations
Mireia Llorens, Víctor Mañosa
We prove that any planar birational integrable map, which preserves a fibration given by genus curves has a Lie symmetry and some associated invariant measures. The obtained re…
Basin of attraction of triangular maps with applications
Anna Cima, Armengol Gasull, Víctor Mañosa
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 dynami…
Global periodicity conditions for maps and recurrences via Normal Forms
Anna Cima, Armengol Gasull, Víctor Mañosa
We 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 Norma…
On periodic solutions of 2-periodic Lyness difference equations
Guy Bastien, Victor Mañosa, Marc Rogalski
We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with…
Non-autonomous 2-periodic Gumovski-Mira difference equations
Anna Cima, Armengol Gasull, Victor Mañosa
We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of t…