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Chaotic Dynamics at the Boundary of a Basin of Attractionvia Non-transversal Intersections for a Non-global SmoothDiffeomorphism

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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 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.

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Journal of Nonlinear Science, 2024, vol. 34

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Chaotic Dynamics at the Boundary of a Basin of Attractionvia Non-transversal Intersections for a Non-global SmoothDiffeomorphism