Chaotic dynamics at the boundary of a basin of attraction via non-transversal intersections for a non-global smooth diffeomorphism

2024/05/14 by Ernest Fontich, Fontich, Ernest, Antonio Garijo +3
Engineering · Mathematics · Physics and Astronomy · #37C05 #37C29 #Dynamical Systems (math.DS) #Elasticity and Wave Propagation #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2405.08812

openalex publication_date 2024/05/14 · openalex created_date 2024/05/16 · openalex updated_date 2026/07/28

Abstract

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 to 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≥ 2 or infinity.

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