{"paper":{"title":"Scarring of quasimodes on hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.AP","authors_text":"Lior Silberman, Suresh Eswarathasan","submitted_at":"2016-09-16T05:24:12Z","abstract_excerpt":"Let $N$ be a compact hyperbolic manifold, $M\\subset N$ an embedded totally geodesic submanifold, and let $-\\hbar^2\\Delta_{N}$ be the semiclassical Laplace--Beltrami operator.\n  For any $\\varepsilon>0$, we explicitly construct families of \\emph{quasimodes} of spectral width at most $\\varepsilon\\frac{\\hbar}{|\\log\\hbar|}$ which exhibit a \"strong scar\" on $M$ in that their microlocal lifts converge weakly to a probability measure which places positive weight on $S^*M$ ($\\hookrightarrow S^*N$). An immediate corollary is that \\emph{any} invariant measure on $S^*N$ occurs in the ergodic decomposition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04912","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"}