Upper, down, two-sided Lorenz attractor, collisions, merging and switching
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| Format: | Preprint |
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2021
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| _version_ | 1866914685209542656 |
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| author | Barros, Diego Bonatti, Christian Pacifico, Maria Jose |
| author_facet | Barros, Diego Bonatti, Christian Pacifico, Maria Jose |
| contents | We present a slightly modified version of the well known "geometric Lorenz attractor". It consists in a C1 open set O of vector fields in R3 having an attracting region U containing: (1) a unique singular saddle point sigma; (2) a unique attractor Lambda containing the singular point; (3) the maximal invariant in U contains at most 2 chain recurrence classes, which are Lambda and (at most) one hyperbolic horseshoe. The horseshoe and the singular attractor have a collision along the union of 2 co-dimension 1 sub-manifolds which divide O in 3 regions. By crossing this collision locus, the attractor and the horseshoe may merge in a two-sided Lorenz attractor, or they may exchange their nature: the Lorenz attractor expel the singular point sigma and becomes a horseshoe and the horseshoe absorbs sigma becoming a Lorenz attractor.
By crossing this collision locus, the attractor and the horseshoe may merge in a two-sided Lorenz attractor, or they may exchange their nature: the Lorenz attractor expel the singular point sigma and becomes a horseshoe and the horseshoe absorbs sigma becoming a Lorenz attractor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2101_07391 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Upper, down, two-sided Lorenz attractor, collisions, merging and switching Barros, Diego Bonatti, Christian Pacifico, Maria Jose Dynamical Systems We present a slightly modified version of the well known "geometric Lorenz attractor". It consists in a C1 open set O of vector fields in R3 having an attracting region U containing: (1) a unique singular saddle point sigma; (2) a unique attractor Lambda containing the singular point; (3) the maximal invariant in U contains at most 2 chain recurrence classes, which are Lambda and (at most) one hyperbolic horseshoe. The horseshoe and the singular attractor have a collision along the union of 2 co-dimension 1 sub-manifolds which divide O in 3 regions. By crossing this collision locus, the attractor and the horseshoe may merge in a two-sided Lorenz attractor, or they may exchange their nature: the Lorenz attractor expel the singular point sigma and becomes a horseshoe and the horseshoe absorbs sigma becoming a Lorenz attractor. By crossing this collision locus, the attractor and the horseshoe may merge in a two-sided Lorenz attractor, or they may exchange their nature: the Lorenz attractor expel the singular point sigma and becomes a horseshoe and the horseshoe absorbs sigma becoming a Lorenz attractor. |
| title | Upper, down, two-sided Lorenz attractor, collisions, merging and switching |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2101.07391 |