{"paper":{"title":"Periodic orbits of the ABC flow with $A=B=C=1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrej Zlato\\v{s}, Jack Xin, Yifeng Yu","submitted_at":"2016-01-12T04:20:40Z","abstract_excerpt":"In this paper, we prove that the ODE system $$ \\begin{align*} \\dot x &=\\sin z+\\cos y\\\\ \\dot y &= \\sin x+\\cos z\\\\ \\dot z &=\\sin y + \\cos x, \\end{align*} $$ whose right-hand side is the Arnold-Beltrami-Childress (ABC) flow with parameters $A=B=C=1$, has periodic orbits on $(2\\pi\\mathbb T)^3$ with rotation vectors parallel to $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$. An application of this result is that the well-known G-equation model for turbulent combustion with this ABC flow on $\\mathbb R^3$ has a linear (i.e., maximal possible) flame speed enhancement rate as the amplitude of the flow grows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02724","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"}