Iteration of MΓΆbius transformations and
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A. Barrlund; H. Wallin; J. Karlsson
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Article
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1997
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Elsevier Science
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English
β 600 KB
Let z0 be an arbitrary point in the complex plane. For each positive integer n we choose sn(z) to be -5/(1 + z) or -0.5/(1 + z) with equal probability. We introduce the orbit (zn)~, where zn = Sn(Zn-1) for n > 1. We prove that with probability one the orbit is attracted to the real axis. In the proo