{"paper":{"title":"Geometry and entropy of generalized rotation sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Wolf, Tamara Kucherenko","submitted_at":"2012-09-29T17:27:18Z","abstract_excerpt":"For a continuous map $f$ on a compact metric space we study the geometry and entropy of the generalized rotation set $\\R(\\Phi)$. Here $\\Phi=(\\phi_1,...,\\phi_m)$ is a $m$-dimensional continuous potential and $\\R(\\Phi)$ is the set of all $\\mu$-integrals of $\\Phi$ and $\\mu$ runs over all $f$-invariant probability measures. It is easy to see that the rotation set is a compact and convex subset of $\\bR^m$. We study the question if every compact and convex set is attained as a rotation set of a particular set of potentials within a particular class of dynamical systems. We give a positive answer in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0135","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"}