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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.01134 |
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| _version_ | 1866915087864823808 |
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| author | Cheng, Junfeng Yang, Xiao-Song |
| author_facet | Cheng, Junfeng Yang, Xiao-Song |
| contents | This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are provided: one from the perturbed Duffing system and another from a polynomial system proposed by Chen, demonstrating the prevalence of semi-horseshoes in chaotic systems. Moreover, the semi-topological horseshoe theory enhances the detection of chaos and improves the accuracy of topological entropy estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incomplete crossing and semi-topological horseshoes Cheng, Junfeng Yang, Xiao-Song Dynamical Systems This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are provided: one from the perturbed Duffing system and another from a polynomial system proposed by Chen, demonstrating the prevalence of semi-horseshoes in chaotic systems. Moreover, the semi-topological horseshoe theory enhances the detection of chaos and improves the accuracy of topological entropy estimation. |
| title | Incomplete crossing and semi-topological horseshoes |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.01134 |