Existence of SRB measures for some Rössler systems
Source: hexagonmath.org/abs/2610.00676v1
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.…
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