{"paper":{"title":"A criterion for zero averages and full support of ergodic measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Bonatti, Jairo Bochi, Lorenzo J. Diaz","submitted_at":"2016-09-25T16:07:27Z","abstract_excerpt":"Consider a homeomorphism $f$ defined on a compact metric space $X$ and a continuous map $\\phi\\colon X \\to \\mathbb{R}$. We provide an abstract criterion, called \\emph{control at any scale with a long sparse tail} for a point $x\\in X$ and the map $\\phi$, that guarantees that any weak$\\ast$ limit measure $\\mu$ of the Birkhoff average of Dirac measures $\\frac1n\\sum_0^{n-1}\\delta(f^i(x))$ is such that $\\mu$-almost every point $y$ has a dense orbit in $X$ and the Birkhoff average of $\\phi$ along the orbit of $y$ is zero.\n  As an illustration of the strength of this criterion, we prove that the diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07764","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"}