{"paper":{"title":"Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hong-Kun Zhang, Matthew Nicol, Meagan Carney","submitted_at":"2017-09-02T03:56:05Z","abstract_excerpt":"We show that a compound Poisson distribution holds for scaled exceedances of observables $\\phi$ uniquely maximized at a periodic point $\\zeta$ in a variety of two-dimensional hyperbolic dynamical systems with singularities $(M,T,\\mu)$, including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form $\\phi (z)=-\\ln d(z,\\zeta)$ where $d$ is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a P\\'olya-Aeppli distibution of index $\\theta$. We calculate $\\theta$ in ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00530","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"}