{"paper":{"title":"Exact Lyapunov exponents of the generalized Boole transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Ken-ichi Okubo, Ken Umeno","submitted_at":"2015-10-29T05:49:40Z","abstract_excerpt":"The generalized Boole transformations have rich behavior ranging from the \\textit{mixing} phase with the Cauchy invariant measure to the \\textit{dissipative} phase through the \\textit{infinite ergodic} phase with the Lebesgue measure. In this Letter, by giving the proof of mixing property for $0<\\alpha<1$ we show an \\textit{analytic} formula of the Lyapunov exponents $\\lambda$ which are explicitly parameterized in terms of the parameter $\\alpha$ of the generalized Boole transformations for the whole region $\\alpha>0$ and bridge those three phase \\textit{continuously}. We found the different sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08569","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"}