{"paper":{"title":"Feral Curves and Minimal Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Helmut Hofer, Joel W. Fish","submitted_at":"2018-12-16T23:06:38Z","abstract_excerpt":"Here we prove that for each Hamiltonian function $H\\in \\mathcal{C}^\\infty(\\mathbb{R}^4, \\mathbb{R})$ defined on the standard symplectic $(\\mathbb{R}^4, \\omega_0)$, for which $M:=H^{-1}(0)$ is a non-empty compact regular energy level, the Hamiltonian flow on $M$ is not minimal. That is, we prove there exists a closed invariant subset of the Hamiltonian flow in $M$ that is neither $\\emptyset$ nor all of $M$. This answers the four dimensional case of a twenty year old question of Michel Herman, part of which can be regarded as a special case of the Gottschalk Conjecture.\n  Our principal technique"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06554","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"}