39 citations · 151 across the 16 of their papers we have counts for
21 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…
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…
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…
On the basin of attraction of a critical three-cycle of a model for the secant map
Ernest Fontic, Antonio Garijo, Xavier Jarque
We consider the secant method applied to a real polynomial of degree as a discrete dynamical system on . If the polynomial has a local extremum at…
Local connectivity of boundaries of tame Fatou components of meromorphic functions
Krzystof Barański, Núria Fagella, Xavier Jarque +1
We prove local connectivity of the boundaries of invariant simply connected attracting basins for a class of transcendental meromorphic maps. The maps within this class need not be…