Paperfolding Structures as Templates for Horseshoes in Multidimensional Hénon Maps
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916944402186240 |
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| author | Li, Jizhou Fujioka, Keisuke Shudo, Akira |
| author_facet | Li, Jizhou Fujioka, Keisuke Shudo, Akira |
| contents | We propose a novel framework for analyzing the geometric structure of horseshoes arising in three- and four-dimensional Hénon-type maps by introducing paperfolding structures as geometric templates. These structures capture the folding and stacking mechanisms characteristic of high-dimensional chaotic dynamics, offering a combinatorial and visual language to describe complex horseshoe formations. By systematically relating iterated paperfolding patterns to the observed geometries in multidimensional maps, our approach provides a concrete method for visualizing and classifying the topological features of chaotic sets in dimensions higher than two. This framework offers new insight into the organization of chaos in higher-dimensional discrete dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paperfolding Structures as Templates for Horseshoes in Multidimensional Hénon Maps Li, Jizhou Fujioka, Keisuke Shudo, Akira Chaotic Dynamics Dynamical Systems We propose a novel framework for analyzing the geometric structure of horseshoes arising in three- and four-dimensional Hénon-type maps by introducing paperfolding structures as geometric templates. These structures capture the folding and stacking mechanisms characteristic of high-dimensional chaotic dynamics, offering a combinatorial and visual language to describe complex horseshoe formations. By systematically relating iterated paperfolding patterns to the observed geometries in multidimensional maps, our approach provides a concrete method for visualizing and classifying the topological features of chaotic sets in dimensions higher than two. This framework offers new insight into the organization of chaos in higher-dimensional discrete dynamical systems. |
| title | Paperfolding Structures as Templates for Horseshoes in Multidimensional Hénon Maps |
| topic | Chaotic Dynamics Dynamical Systems |
| url | https://arxiv.org/abs/2509.08251 |