{"paper":{"title":"Plaque Inverse Limit of a Dynamical System - Dynamics, Signatures and Local Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DS","authors_text":"Avraham Goldstein","submitted_at":"2015-02-09T03:48:08Z","abstract_excerpt":"The Plaque Inverse Limit of a branched covering self-map of a Riemann surface was introduced and studied in \\cite{CCG}. A point $x$ of P.I.L. was called regular if P.I.L. has the natural Riemann Surface structure at $x$ and was called irregular otherwise. The notion of the signature $sign(x,c)$ of $x$ with respect to a critical point $c$, which was shown to be a local invariant of P.I.L. was introduced and developed. It was shown that $sign(x,c)$ is nontrivial for some critical points $c$ if and only if $x$ is an irregular point. It was shown that the local topology of P.I.L. at an irregular p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02345","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"}