{"paper":{"title":"Smooth Hamilton-Jacobi solutions for the Horocycle flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Luca Asselle","submitted_at":"2016-02-16T13:27:50Z","abstract_excerpt":"In this paper we compute all the smooth solutions to the Hamilton-Jacobi equation associated with the horocycle flow. This can be seen as the Euler-Lagrange flow (restricted to the energy level set $E^{-1}(\\frac 12)$) defined by the Tonelli Lagrangian $L:T\\mathbb H\\rightarrow \\mathbb R$ given by (hyperbolic) kinetic energy plus the standard magnetic potential. The method we use is to look at Lagrangian graphs that are contained in the level set $\\{H=\\frac 12\\}$, where $H:T^*\\mathbb H\\rightarrow \\mathbb R$ denotes the Hamiltonian dual to $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05011","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"}