{"paper":{"title":"The projective translation equation and rational plane flows. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP"],"primary_cat":"math.CA","authors_text":"Giedrius Alkauskas","submitted_at":"2012-01-04T14:14:43Z","abstract_excerpt":"Let X=(x,y). A plane flow is a function F(X,t): R^2*R->R^2 such that F(F(X,s),t)=F(X,s+t) for (almost) all real numbers x,y,s,t (the function F might not be well-defined for certain x,y,t). In this paper we investigate rational plane flows which are of the form F(X,t)=f(Xt)/t; here f is a pair of rational functions in 2 real variables. These may be called projective flows, and for a description of such flows only the knowledge of Cremona group in dimension 1 is needed. Thus, the aim of this work is to completely describe over R all rational solutions of the two dimensional translation equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0894","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"}