Chaotic Dynamics at the Boundary of a Basin of Attractionvia Non-transversal Intersections for a Non-global SmoothDiffeomorphism
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...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/218959 |
| Acesso em linha: | https://hdl.handle.net/2445/218959 |
| Access Level: | acceso abierto |
| Palavra-chave: | Varietats (Matemàtica) Sistemes dinàmics hiperbòlics Manifolds (Mathematics) Hyperbolic dynamical systems |
| Resumo: | 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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