{"paper":{"title":"Strange non-chaotic attractors in quasiperiodically forced circle maps: Diophantine forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"T. J\\\"ager","submitted_at":"2011-02-22T10:21:02Z","abstract_excerpt":"We study parameter families of quasiperiodically forced (qpf) circle maps with Diophantine frequency. Under certain C1-open conditions concerning their geometry, we prove that these families exhibit nonuniformly hyperbolic behaviour, often referred to as the existence of strange nonchaotic attractors, on parameter sets of positive measure. This provides a nonlinear version of results by Young on quasiperiodic SL (2;R)-cocycles and complements previous results in this direction which hold for sets of frequencies of positive measure, but did not allow for an explicit characterisation of these fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4443","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"}