{"paper":{"title":"Ergodic Transformations of the Space of $p$-adic Integers","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Vladimir Anashin","submitted_at":"2006-02-05T14:58:41Z","abstract_excerpt":"Let $\\mathcal L_1$ be the set of all mappings $f\\colon\\Z_p\\Z_p$ of the space of all $p$-adic integers $\\Z_p$ into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping $f\\in\\mathcal L_1$ is ergodic with respect to the normalized Haar measure on $\\Z_p$ if and only if $f$ induces a single cycle permutation on each residue ring $\\Z/p^k\\Z$ modulo $p^k$, for all $k=1,2,3,...$. The multivariate case, as well as measure-preserving mappings, are considered also.\n  Results of the paper in a combination with earlier results of the author give explicit description of ergodi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602083","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"}