{"paper":{"title":"Fractal properties of Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Domagoj Vlah, Luka Korkut, Vesna Zupanovic","submitted_at":"2013-04-05T16:58:31Z","abstract_excerpt":"A fractal oscillatority of solutions of second-order differential equations near infinity is measured by oscillatory and phase dimensions. The phase dimension is defined as a box dimension of the trajectory $(x,\\dot{x})$ in $\\mathbb{R}^2$ of a solution $x=x(t)$, assuming that $(x,\\dot{x})$ is a spiral converging to the origin. In this work, we study the phase dimension of the class of second-order nonautonomous differential equations with oscillatory solutions including the Bessel equation. We prove that the phase dimension of Bessel functions is equal to 4/3, and that the corresponding trajec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1762","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"}