{"paper":{"title":"Degree, mixing, and absolutely continuous spectrum of cocycles with values in compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.DS","authors_text":"Rafael Tiedra de Aldecoa","submitted_at":"2016-05-13T14:49:09Z","abstract_excerpt":"We consider skew products $$T_\\phi:X\\times G\\to X\\times G,~~(x,g)\\mapsto(F_1(x),g\\;\\!\\phi(x)),$$ where $X$ is a compact manifold with probability measure, $G$ a compact Lie group with Lie algebra $\\frak g$, $F_1:X\\to X$ the time-one map of a measure-preserving flow, and $\\phi\\in C^1(X,G)$ a cocycle. Then, we define the degree of $\\phi$ as a suitable function $P_\\phi M_\\phi:X\\to\\frak g$, we show that it transforms in a natural way under Lie group homomorphisms and under the relation of $C^1$-cohomology, and we explain how it generalises previous definitions of degree of a cocycle. For each fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04198","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"}