{"id":"hexagon/2610.00676","pdf":"https://hexagonmath.org/pdf/2610.00676v1","url":"https://hexagonmath.org/abs/2610.00676v1","tags":["math.DG","msc:37D45","Rossler system"],"score":0,"title":"Existence of SRB measures for some Rössler systems","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Theophile Caby"],"reviews":0,"subject":"math.DS","summary":"We prove that for the Rössler systemẋ = −(y + z),ẏ = x + ay,ż = b + z(x − c) with a = b = 0.2, the set of parameters c within 6 · 10 −5 of the classical value c = 5.7 for which the ow has a Hénon-like strange attractor supporting a SinaiRuelleBowen (SRB) measure has positive Lebesgue measure. The key step, proved with computer assistance, is that at an explicit parameter within 5.5 · 10 −5 of 5.7 the period-one saddle of the Poincaré map has a quadratic homoclinic tangency that unfolds generically; the conclusion then follows from the theorems of MoraViana, BenedicksYoung and BenedicksViana.…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}