From the 1 of 6 linked papers with an AI index.
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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…
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…