Locally contractive iterated function systems
An iterated function system on \(X\subset \mathbb{R}^d\) is defined by successively applying and i.i.d. sequence of random Lipschitz functions from \(X\) to \(X\). This paper shows how \(F_n=f_1 \circ\cdots \circ f_n\) may converge even in the absence of the strong contraction conditions, for instance, Lipschitz constant smaller than 1 on average, which earlier work has required. Instead, it is required that there be a region of contraction which compensates for the noncontractive or even expansive part of the functions. Applications to queues, to self-modifying random walks and random logistic maps are given.
scientific article; zbMATH DE number 1496115