The slow recurrence and stochastic stability of unimodal interval maps with wild attractors (Q2839488)

For a \(C^3\) unimodal interval map \(f\) with a non-flat critical point, only hyperbolic repelling periodic points, and a wild attractor, the authors prove that \(f\) satisfies the slow recurrence condition of \textit{M. Tsujii} [Random Comput. Dyn. 1, No. 1, 59--89 (1993; Zbl 0783.58018)]. In addition to this, they prove that \(f\) is stochastically stable in their main theorem. The authors also show that if \(c\) satisfies the slow recurrence condition, \(f\) has no absolutely continuous invariant probability measure, and \(f|_{\omega(c)}\) is uniquely ergodic, then \(f\) has a unique SRB measure supported on \(\omega(c)\) and \(f\) is stochastically stable.