{"paper":{"title":"Eigenvalues, K-theory and Minimal Flows","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Benjam\\'in Itz\\'a-Ortiz","submitted_at":"2004-10-19T18:44:30Z","abstract_excerpt":"Let $(Y,T)$ be a minimal suspension flow built over a dynamical system $(X,S)$ and with (strictly positive, continuous) ceiling function $f\\colon X\\to\\R$. We show that the eigenvalues of $(Y,T)$ are contained in the range of a trace on the $K_0$-group of $(X,S)$. Moreover, a trace gives an order isomorphism of a subgroup of $K_0(C(X)\\rtimes_S\\mathbb{Z})$ with the group of eigenvalues of $(Y,S)$. Using this result, we relate the values of $t$ for which the time-$t$ map on minimal suspension flow is minimal, with the $K$-theory of the base of this suspension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410426","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"}