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Main Authors: Li, Jizhou, Fujioka, Keisuke, Shudo, Akira
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2509.08251
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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