{"paper":{"title":"On the computability of rotation sets and their entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Wolf, Martin Schmoll, Michael Burr","submitted_at":"2017-06-24T15:41:06Z","abstract_excerpt":"Given a continuous dynamical system $f:X\\to X$ on a compact metric space $X$ and an $m$-dimensional continuous potential $\\Phi:X\\to \\mathbb R^m$, the (generalized) rotation set ${\\rm Rot}(\\Phi)$ is defined as the set of all $\\mu$-integrals of $\\Phi$, where $\\mu$ runs over all invariant probability measures. Analogous to the classical topological entropy, one can associate the localized entropy ${\\mathcal H}(w)$ to each $w\\in {\\rm Rot}(\\Phi)$. In this paper, we study the computability of rotation sets and localized entropy functions by deriving conditions that imply their computability. We then"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07973","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"}