From the 1 of 6 linked papers with an AI index.
6 papers
A convex-geometric framework for fully phase-locked states in the finite Kuramoto model
Antonio Garijo, Sergio Gómez, Alex Arenas
The paper analyzes the finite-size Kuramoto model and derives a convex‑geometric description of the minimal coupling needed for all oscillators to lock in phase, providing an expli…
Mersenne numbers and the doubling map
LluÃs AlsedÃ, 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…
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…
Connected McMullen-like Julia sets in a Chebyshev-Halley Family
Jordi Canela, Antonio Garijo, Pascale Roesch
In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where th…
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 con…