{"paper":{"title":"Higher dimensional shrinking target problem in beta dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Mumtaz Hussain, Weiliang Wang","submitted_at":"2019-08-06T12:07:16Z","abstract_excerpt":"We consider the two dimensional shrinking target problem in the beta dynamical system for general $\\beta>1$ and with the general error of approximations. Let $f, g$ be two positive continuous functions. For any $x_0,y_0\\in[0,1]$, define the shrinking target set\n  $$ E(T_\\beta, f,g):=\\left\\{(x,y)\\in [0,1]^2: \\begin{array}{ll} |T_{\\beta}^{n}x-x_{0}|<e^{-S_nf(x)}\\\\ [1ex] |T_{\\beta}^{n}y-y_{0}|< e^{-S_ng(y)} \\end{array} \\ {\\text{for infinitely many}} \\ n\\in \\N \\right\\}, $$ where $S_nf(x)=\\sum_{j=0}^{n-1}f(T_\\beta^jx)$ is the Birkhoff sum. We calculate the Hausdorff dimension of this set and prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02098","kind":"arxiv","version":2},"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/1908.02098/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"}