Forward Iterated Function Systems
نویسنده
چکیده
Abstract We consider the iterated function system Fn = fn ◦ . . . ◦ f2 ◦ f1 formed from the holomorphic functions in the family H(∆,Ω). The analog of stable behavior for such systems is that the limit functions be constant. We prove that a necessary and sufficient condition for stable behavior for all iterated function systems formed from H(∆, Ω) is that Ω be a proper subset of ∆. We also prove that for a given iterated function system the constant limit functions are unique if and only if Ω is relatively compact in ∆.
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