Iteration of Möbius transformations and attractors on the real line

✍ Scribed by A. Barrlund; H. Wallin; J. Karlsson

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 600 KB
• Volume: 33
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(96)00215-5

✦ Synopsis

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 proof, we have to do some calculations on a computer.