{"paper":{"title":"Smooth ergodic theory of $\\mathbb{Z}^d$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang","submitted_at":"2016-10-31T16:14:24Z","abstract_excerpt":"In the first part of this paper, we formulate a general setting in which to study the ergodic theory of differentiable $\\mathbb{Z}^d$-actions preserving a Borel probability measure. This framework includes actions by $C^{1+\\text{H\\\"older}}$ diffeomorphisms of compact manifolds. We construct intermediate and coarse unstable manifolds for the action and establish controls on their local geometry.\n  In the second part we consider the relationship between entropy, Lyapunov exponents, and the geometry of conditional measures for rank-1 systems given by a number of generalizations of the Ledrappier-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09997","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"}