Fontich, Ernest, 1955-Garijo Real, AntonioJarque i Ribera, Xavier2025-02-192025-02-192024-09-010938-8974https://hdl.handle.net/2445/218959In 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 come out as a truncated map governing the local dynamics near a critical period three-cycle associated with the Secant map. Using Moser's version of Birkhoff-Smale's theorem, we prove that the boundary of the basin of attraction of the origin contains a Cantor-like invariant subset such that the restricted dynamics to it is conjugate to the full shift of $N$-symbols for any integer $N \geq 2$ or infinity.32 p.application/pdfengcc by (c) Ernest Fontich et al., 2024http://creativecommons.org/licenses/by/3.0/es/Varietats (Matemàtica)Sistemes dinàmics hiperbòlicsManifolds (Mathematics)Hyperbolic dynamical systemsinfo:eu-repo/semantics/article7519852025-02-19info:eu-repo/semantics/openAccess