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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.30064 |
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| _version_ | 1866910270280957952 |
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| author | Winsor, Karl |
| author_facet | Winsor, Karl |
| contents | We study the action of the Hecke triangle groups $G_q$ on $λ_q \mathbb{Q}(λ_q^2) \cup \{\infty\}$ with $λ_q = 2 \cos (π/ q)$. When $q = 18$, we show the existence of infinitely many distinct orbits of fixed points of special hyperbolic elements of $G_q$. We also find new orbits for several other values of $q$. These results provide new examples of special affine pseudo-Anosov homeomorphisms on the unfoldings of regular $q$-gons. In particular, on the unfolding of the regular $18$-gon, there are infinitely many distinct Veech group orbits of directions invariant under a special affine pseudo-Anosov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30064 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hecke Triangle Groups and Special Hyperbolic Elements Winsor, Karl Dynamical Systems We study the action of the Hecke triangle groups $G_q$ on $λ_q \mathbb{Q}(λ_q^2) \cup \{\infty\}$ with $λ_q = 2 \cos (π/ q)$. When $q = 18$, we show the existence of infinitely many distinct orbits of fixed points of special hyperbolic elements of $G_q$. We also find new orbits for several other values of $q$. These results provide new examples of special affine pseudo-Anosov homeomorphisms on the unfoldings of regular $q$-gons. In particular, on the unfolding of the regular $18$-gon, there are infinitely many distinct Veech group orbits of directions invariant under a special affine pseudo-Anosov. |
| title | Hecke Triangle Groups and Special Hyperbolic Elements |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.30064 |