Bicycle tracks with hyperbolic monodromy -- results and conjectures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913636005445632 |
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| author | Bor, G. Hernández-Lamoneda, L. Tabachnikov, S. |
| author_facet | Bor, G. Hernández-Lamoneda, L. Tabachnikov, S. |
| contents | We find new necessary and sufficient conditions for the bicycling monodromy of a closed plane curve to be hyperbolic. Our main tool is the ``hyperbolic development" interpretation of the bicycling monodromy of plane curves. Based on computer experiments, we pose two conjectures concerning the bicycling monodromy of strictly convex closed plane curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bicycle tracks with hyperbolic monodromy -- results and conjectures Bor, G. Hernández-Lamoneda, L. Tabachnikov, S. Differential Geometry Classical Analysis and ODEs 53A04 We find new necessary and sufficient conditions for the bicycling monodromy of a closed plane curve to be hyperbolic. Our main tool is the ``hyperbolic development" interpretation of the bicycling monodromy of plane curves. Based on computer experiments, we pose two conjectures concerning the bicycling monodromy of strictly convex closed plane curves. |
| title | Bicycle tracks with hyperbolic monodromy -- results and conjectures |
| topic | Differential Geometry Classical Analysis and ODEs 53A04 |
| url | https://arxiv.org/abs/2412.18676 |