Chaotic dynamics at the boundary of a basin of attraction via non-transversal intersections for a non-global smooth diffeomorphism
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| Format: | Preprint |
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2024
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| _version_ | 1866911876799004672 |
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| author | Fontich, Ernest Garijo, Antonio Jarque, Xavier |
| author_facet | Fontich, Ernest Garijo, Antonio Jarque, Xavier |
| contents | 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 $N\ge 2$ or infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chaotic dynamics at the boundary of a basin of attraction via non-transversal intersections for a non-global smooth diffeomorphism Fontich, Ernest Garijo, Antonio Jarque, Xavier Dynamical Systems 37C05, 37C29 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 $N\ge 2$ or infinity. |
| title | Chaotic dynamics at the boundary of a basin of attraction via non-transversal intersections for a non-global smooth diffeomorphism |
| topic | Dynamical Systems 37C05, 37C29 |
| url | https://arxiv.org/abs/2405.08812 |