{"paper":{"title":"Measure rigidity for random dynamics on surfaces with positive entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aaron W. Brown, Federico Rodriguez Hertz","submitted_at":"2014-06-27T14:44:40Z","abstract_excerpt":"Given a surface $M$ and a Borel probability measure $\\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\\nu$-stationary probability measures on $M$. Assuming the positivity of a certain entropy, the following dichotomy is proved: either the stable distributions for the random dynamics is non-random, or the measure is SRB. In the case that $\\nu$-a.e. diffeomorphism preserves a common smooth measure $m$, we show that for any positive-entropy stationary measure $\\mu$, either there exists a $\\nu$-almost surely invariant $\\mu$-measurable line field (corresponding do the stable distributio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7201","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"}