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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05735 |
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| _version_ | 1866913808976445440 |
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| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
| contents | We study the $(k+1,k)$ diagonal map for $k=2,3,4,...$. We call this map $Δ_k$. The map $Δ_1$ is the pentagram map and $Δ_k$ is a generalization. $Δ_k$ does not preserve convexity, but we prove that $Δ_k$ preserves a subset $B_k$ of certain star-shaped polygons which we call $k$-birds. The action of $Δ_k$ on $B_k$ seems similar to the action of $Δ_1$ on the space of convex polygons. We show that some classic geometric results about $Δ_1$ generalize to this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Flapping Birds in the Pentagram Zoo Schwartz, Richard Evan Dynamical Systems Combinatorics We study the $(k+1,k)$ diagonal map for $k=2,3,4,...$. We call this map $Δ_k$. The map $Δ_1$ is the pentagram map and $Δ_k$ is a generalization. $Δ_k$ does not preserve convexity, but we prove that $Δ_k$ preserves a subset $B_k$ of certain star-shaped polygons which we call $k$-birds. The action of $Δ_k$ on $B_k$ seems similar to the action of $Δ_1$ on the space of convex polygons. We show that some classic geometric results about $Δ_1$ generalize to this setting. |
| title | The Flapping Birds in the Pentagram Zoo |
| topic | Dynamical Systems Combinatorics |
| url | https://arxiv.org/abs/2403.05735 |