{"paper":{"title":"Multifractal analysis of some multiple ergodic averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ai-Hua Fan (LAMFA), Joerg Schmeling, Meng Wu (LAMFA)","submitted_at":"2012-12-12T10:37:52Z","abstract_excerpt":"In this paper we study the multiple ergodic averages $$ \\frac{1}{n}\\sum_{k=1}^n \\varphi(x_k, x_{kq}, ..., x_{k q^{\\ell-1}}), \\qquad (x_n) \\in \\Sigma_m $$ on the symbolic space $\\Sigma_m ={0, 1, ..., m-1}^{\\mathbb{N}^*}$ where $m\\ge 2, \\ell\\ge 2, q\\ge 2$ are integers. We give a complete solution to the problem of multifractal analysis of the limit of the above multiple ergodic averages. Actually we develop a non-invariant and non-linear version of thermodynamic formalism that is of its own interest. We study a large class of measures (called telescopic measures) and the special case of telescop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2764","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"}