Saberi, A.A.Tirnakli, U.Tsallis, C.2025-12-302025-12-3020252470-0045https://doi.org/10.1103/gtlz-67cfhttps://hdl.handle.net/20.500.14365/8482We focus on the Feigenbaum-Coullet-Tresser point of the dissipative one-dimensional z-logistic map xt+1=1−a|xt|z(z≥1). We show that sums of iterates converge to q-Gaussian distributions Pq(y)=Pq(0)expq(−βqy2)=Pq(0)[1+(q−1)βqy2]1/(1−q)(q≥1;βq>0), which optimize the nonadditive entropic functional Sq under simple constraints. We propose and justify heuristically a closed-form prediction for the entropic index, q(z)=1+2/(z+1), and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z>2 and divergent variance for 1≤z≤2. These results extend edge-of-chaos central limit behavior beyond the standard (z=2) case and provide a simple predictive law for unimodal maps with varying maximum order. © 2025 authors. Published by the American Physical Society.eninfo:eu-repo/semantics/openAccessArticle10.1103/gtlz-67cf2-s2.0-105024077917