{"paper":{"title":"Hecke Triangle Groups and Special Hyperbolic Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Karl Winsor","submitted_at":"2026-05-28T15:14:07Z","abstract_excerpt":"We study the action of the Hecke triangle groups $G_q$ on $\\lambda_q \\mathbb{Q}(\\lambda_q^2) \\cup \\{\\infty\\}$ with $\\lambda_q = 2 \\cos (\\pi / q)$. 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 spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30064","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}