{"paper":{"title":"Wavy spirals and their fractal connection with chirps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Darko Zubrinic, Domagoj Vlah, Luka Korkut, Vesna Zupanovic","submitted_at":"2012-10-24T17:35:42Z","abstract_excerpt":"We study the fractal oscillatority of a class of real $C^1$ functions $x=x(t)$ near $t=\\infty$. It is measured by oscillatory and phase dimensions, defined as box dimensions of the graph of $X(\\tau)=x(\\frac{1}{\\tau})$ near $\\tau=0$ and the trajectory $(x,\\dot{x})$ in $\\mathbb{R}^2$, respectively, assuming that $(x,\\dot{x})$ is a spiral converging to the origin. The relationship between these two dimensions has been established for a class of oscillatory functions using formulas for box dimensions of graphs of chirps and nonrectifiable wavy spirals, introduced in this paper. Wavy spirals are a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6611","kind":"arxiv","version":3},"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"}