{"paper":{"title":"Trivial and simple spectrum for SL(2,R) cocycles with free base and fiber dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mario Bessa, Paulo Varandas","submitted_at":"2012-09-11T11:53:09Z","abstract_excerpt":"Let $AC_D(M,SL(2,\\mathbb R))$ denote the pairs $(f,A)$ so that $f\\in \\mathcal A\\subset \\text{Diff}^{1}(M)$ is a $C^{1}$-Anosov transitive diffeomorphisms and $A$ is an $SL(2,\\mathbb R)$ cocycle dominated with respect to $f$. We prove that open and densely in $AC_D(M,SL(2,\\mathbb R))$ (in appropriate topologies) the pair $(f,A)$ has simple spectrum with respect to the unique maximal entropy measure $\\mu_f$. On the other hand, there exists a residual subset $\\mathcal{R}\\subset \\text{Aut}_{Leb}(M)\\times L^\\infty(M,SL(2,\\mathbb R))$, with respect to the separate topology, such that any element $(f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2293","kind":"arxiv","version":3},"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"}