High order homoclinic tangencies of corank 2
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909169158717440 |
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| author | Mints, Dmitrii |
| author_facet | Mints, Dmitrii |
| contents | We prove that in the space of $C^r$ maps $(r=2,\ldots,\infty,ω)$ of a smooth manifold of dimension at least 4 there exist open regions where maps with infinitely many corank-2 homoclinic tangencies of all orders are dense. The result is applied to show the existence of maps with universal two-dimensional dynamics, i.e. maps whose iterations approximate the dynamics of every map of a two-dimensional disk with an arbitrarily good accuracy. We show that maps with universal two-dimensional dynamics are $C^r$-generic in the regions under consideration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High order homoclinic tangencies of corank 2 Mints, Dmitrii Dynamical Systems We prove that in the space of $C^r$ maps $(r=2,\ldots,\infty,ω)$ of a smooth manifold of dimension at least 4 there exist open regions where maps with infinitely many corank-2 homoclinic tangencies of all orders are dense. The result is applied to show the existence of maps with universal two-dimensional dynamics, i.e. maps whose iterations approximate the dynamics of every map of a two-dimensional disk with an arbitrarily good accuracy. We show that maps with universal two-dimensional dynamics are $C^r$-generic in the regions under consideration. |
| title | High order homoclinic tangencies of corank 2 |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.08989 |