Locally Contractive Iterated Function Systems
نویسنده
چکیده
An iterated function system on X R d is deened by successively iterating an i.i.d. sequence of random Lipschitz functions from X to X. This paper shows how Fn = f 1 fn 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 posited that there be a region of contraction which compensates for the non-contractive or even expansive part of the functions. Applications to self-modifying random walks and to random logistic maps are given.
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