{"paper":{"title":"Dynamical properties of the negative beta transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Wolfgang Steiner (LIAFA)","submitted_at":"2011-01-12T14:01:55Z","abstract_excerpt":"We analyse dynamical properties of the negative beta transformation, which has been studied recently by Ito and Sadahiro. Contrary to the classical beta transformation, the density of the absolutely continuous invariant measure of the negative beta transformation may be zero on certain intervals. By investigating this property in detail, we prove that the $(-\\beta)$-transformation is exact for all $\\beta>1$, confirming a conjecture of G\\'ora, and intrinsic, which completes a study of Faller. We also show that the limit behaviour of the $(-\\beta)$-expansion of 1 when $\\beta$ tends to 1 is relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2366","kind":"arxiv","version":3},"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"}