An algorithm to detect and rigorously verify blenders
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912984159223808 |
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| author | Hammerlindl, Andy McAlister, Natalia Tucker, Warwick |
| author_facet | Hammerlindl, Andy McAlister, Natalia Tucker, Warwick |
| contents | We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a rough approximation of the strong unstable direction in a prescribed region. Since our approach does not rely on precise data, such as the exact location of invariant manifolds or fixed points, it provides a systematic framework to verify blenders in explicit examples. Here, we apply this framework to rigorously verify that a family of three-dimensional Hénon-like maps presents blenders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21603 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An algorithm to detect and rigorously verify blenders Hammerlindl, Andy McAlister, Natalia Tucker, Warwick Dynamical Systems 37D30, 37M21, 65G20 We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a rough approximation of the strong unstable direction in a prescribed region. Since our approach does not rely on precise data, such as the exact location of invariant manifolds or fixed points, it provides a systematic framework to verify blenders in explicit examples. Here, we apply this framework to rigorously verify that a family of three-dimensional Hénon-like maps presents blenders. |
| title | An algorithm to detect and rigorously verify blenders |
| topic | Dynamical Systems 37D30, 37M21, 65G20 |
| url | https://arxiv.org/abs/2603.21603 |