{"paper":{"title":"Generalization of the Gauss Map: A jump into chaos with universal features","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Christian Beck, Constantino Tsallis, Ugur Tirnakli","submitted_at":"2024-11-20T15:18:33Z","abstract_excerpt":"The Gauss map (or continued fraction map) is an important dissipative one-dimensional discrete-time dynamical system that exhibits chaotic behaviour and which generates a symbolic dynamics consisting of infinitely many different symbols. Here we introduce a generalization of the Gauss map which is given by $x_{t+1}=\\frac{1}{x_t^\\alpha} - \\Bigl[\\frac{1}{x_t^\\alpha} \\Bigr]$ where $\\alpha \\geq 0$ is a parameter and $x_t \\in [0,1]$ ($t=0,1,2,3,\\ldots$). The symbol $[\\dots ]$ denotes the integer part. This map reduces to the ordinary Gauss map for $\\alpha=1$. The system exhibits a sudden `jump into"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13629","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/2411.13629/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"}