{"paper":{"title":"Generalized Attracting Horseshoe in the R\\\"{o}ssler Attractor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aminur Rahman, Denis Blackmore, Ian Jordan, Karthik Murthy, Parth Sojitra","submitted_at":"2018-11-15T09:45:59Z","abstract_excerpt":"We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations - realizable by a rather simple electronic circuit - capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincar\\'{e} section yielding the desired map is described, but not pursued due to its complexity, which makes the construction of a circuit realization exceedingly difficult. Instead, the generalized attracting horseshoe and its trapping region is obtained by using a carefully chosen Poincar\\'{e} map of the R\\\"{o}ssler attractor. Novel numer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06257","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"}