Shen, Weixiao On stochastic stability of non-uniformly expanding interval maps. (English) Zbl 1290.37022 Proc. Lond. Math. Soc. (3) 107, No. 5, 1091-1134 (2013). Let \(f:[0,1]\to [0,1]\) be \(C^3\) multimodal interval map with no attracting cycles and non-flat critical points. Further, assume that the function satisfies a summability condition of exponent one, i.e., \(\sum_{n=0}^\infty \frac{1}{|D^n(f(v))|}<\infty\) for any critical value \(v\). Choose independent random maps \(g_n\) from a space \(\Omega\) containing \(f\) which may be in some case a small neighbourhood of \(f\) in the \(C^2\) topology. Then under general conditions on the perturbations, a typical random orbit \(g_n\circ ...\circ g_0(x)\) has “roughly the same distribution as a typical orbit of \(f\)” or more precisely, strong stochastic stability is shown. Reviewer: Katarina Janková (Bratislava) Cited in 1 ReviewCited in 5 Documents MSC: 37E05 Dynamical systems involving maps of the interval 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37C75 Stability theory for smooth dynamical systems 37H99 Random dynamical systems Keywords:expanding interval maps; random iterates; ergodicity; absolutely continuous invariant measure; strong stochastic stability PDFBibTeX XMLCite \textit{W. Shen}, Proc. Lond. Math. Soc. (3) 107, No. 5, 1091--1134 (2013; Zbl 1290.37022) Full Text: DOI arXiv