11 citations · 51 across the 16 of their papers we have counts for
20 papers
Mersenne numbers and the doubling map
Lluís Alsedà, Antonio Garijo, Xavier Jarque
We study the connection between the Mersenne numbers and the dynamics of the angle-doubling map. Within this framework, we develop an algorithm to compute divisors o…
A convex-geometric framework for fully phase-locked states in the finite Kuramoto model
Antonio Garijo, Sergio Gómez, Alex Arenas
We study the finite-size Kuramoto model of all-to-all coupled phase oscillators with heterogeneous natural frequencies and characterize the minimal coupling strength required for t…
Boundedness and simple connectivity of the basins of attraction for some numerical methods
Jordi Canela, Antonio Garijo, Xavier Jarque
In this paper we study the dynamics of Halley's and Traub's root-finding algorithms applied to a symmetric family of polynomials of degree . We discuss the (un)boundedne…
Dynamics of a Family of Rational Operators of Arbitrary Degree
Beatriz Campos, Jordi Canela, Antonio Garijo +1
In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to red…
On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
Jordi Canela, Vasiliki Evdoridou, Antonio Garijo +1
In this paper we study the dynamics of damped Traub's methods when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which cont…
Chaotic dynamics at the boundary of a basin of attraction via non-transversal intersections for a non-global smooth diffeomorphism
Ernest Fontich, Antonio Garijo, Xavier Jarque
In this paper we give analytic proofs of the existence of transversal homoclinic points for a family of non-globally smooth diffeomorphisms having the origin as a fixed point which…