{"paper":{"title":"A QRT-system of two order one homographic difference equations: conjugation to rotations, periods of periodic solutions, sensitiveness to initial conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guy Bastien, Marc Rogalski","submitted_at":"2014-07-03T13:33:00Z","abstract_excerpt":"We study the homographic system u(n+1)u(n)=c+d/v(n), v(n+1)v(n)=c+d/u(n+1) in the positive quadrant. The orbit of a point is contained in an invariant cubic curve, and the restriction to the positive part of this cubic of the associated dynamical system is conjugated to a rotation on the circle. For a dense invariant set of initial points the solutions are periodic, and if c=1 (this is always possible) every integer n\\geq N(d) is the minimal period of some periodic solution. Every n\\geq 11 is the minimal period of some solution for some d>0, and we find exactly the set of such minimal periods "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0918","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"}