{"paper":{"title":"Displacement sequence of an orientation preserving circle homeomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Justyna Signerska, Wac{\\l}aw Marzantowicz","submitted_at":"2012-10-12T15:51:40Z","abstract_excerpt":"We give a complete description of the behaviour of the sequence of displacements $\\eta_n(z)=\\Phi^n(x) - \\Phi^{n-1}(x) \\ \\rmod \\ 1$, $z=\\exp(2\\pi \\rmi x)$, along a trajectory $\\{\\varphi^{n}(z)\\}$, where $\\varphi$ is an orientation preserving circle homeomorphism and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ its lift. If the rotation number $\\varrho(\\varphi)=\\frac{p}{q}$ is rational then $\\eta_n(z)$ is asymptotically periodic with semi-period $q$. This convergence to a periodic sequence is uniform in $z$ if we admit that some points are iterated backward instead of taking only forward iterations for all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3556","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":""},"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"}