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math.DS2024
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…
math.DS2024
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…