{"paper":{"title":"Diffraction of return time measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Arne Mosbach, Malte Steffens, Marc Kesseb\\\"ohmer, Tony Samuel","submitted_at":"2018-01-23T15:15:57Z","abstract_excerpt":"Letting $T$ denote an ergodic transformation of the unit interval and letting $f \\colon [0,1)\\to \\mathbb{R}$ denote an observable, we construct the $f$-weighted return time measure $\\mu_y$ for a reference point $y\\in[0,1)$ as the weighted Dirac comb with support in $\\mathbb{Z}$ and weights $f \\circ T^z(y)$ at $z\\in\\mathbb{Z}$, and if $T$ is non-invertible, then we set the weights equal to zero for all $z < 0$. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges from the Fourier transform of its autocorrelation and analyse it for the dependence on the underlying"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07608","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"}