{"paper":{"title":"Aperiodicity at the boundary of chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ana Rechtman, Steven Hurder","submitted_at":"2016-03-25T11:02:06Z","abstract_excerpt":"We consider the dynamical properties of $C^{\\infty}$-variations of the flow on an aperiodic Kuperberg plug ${\\mathbb K}$. Our main result is that there exists a smooth 1-parameter family of plugs ${\\mathbb K}_{\\epsilon}$ for $\\epsilon \\in (-a,a)$ and $a<1$, such that: (1) The plug ${\\mathbb K}_0 = {\\mathbb K}$ is a generic Kuperberg plug; (2) For $\\epsilon <0$, the flow in the plug ${\\mathbb K}_{\\epsilon}$ has two periodic orbits that bound an invariant cylinder, all other orbits of the flow are wandering, and the flow has topological entropy zero; (3) For $\\epsilon > 0$, the flow in the plug "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07877","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":""},"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"}