{"paper":{"title":"Random Iteration of Cylinder Maps and diffusive behavior away from resonances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marcel Guardia, Oriol Castej\\'on, Vadim Kaloshin","submitted_at":"2017-05-24T21:13:27Z","abstract_excerpt":"In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: let $(\\theta,r)\\in \\mathbb T\\times \\mathbb R=\\mathbb A$ and \\[ f_{\\pm 1}: \\left(\\begin{array}{c}\\theta\\\\r\\end{array}\\right) \\longmapsto \\left(\\begin{array}{c}\\theta+r+\\varepsilon u_{\\pm 1}(\\theta,r) \\\\ r+\\varepsilon v_{\\pm 1}(\\theta,r) \\end{array}\\right), \\] where $u_\\pm$ and $v_\\pm$ are smooth and $v_\\pm$ are trigonometric polynomials in $\\theta$ such that $\\int v_\\pm(\\theta,r)\\,d\\theta=0$ for each $r$. We study the random compositions \\[ (\\theta_n,r_n)=f_{\\omega_{n-1}}\\circ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09571","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"}