{"paper":{"title":"Mapping densities in a noisy state space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Domenico Lippolis","submitted_at":"2013-03-05T07:41:11Z","abstract_excerpt":"Weak noise smooths out fractals in a chaotic state space and introduces a maximum attainable resolution to its structure. The balance of noise and deterministic stretching/contraction in each neighborhood introduces local invariants of the dynamics that can be used to partition the state space. We study the local discrete-time evolution of a density in a two-dimensional hyperbolic state space, and use the asymptotic eigenfunctions for the noisy dynamics to formulate a new state space partition algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0951","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"}