ITERATION OF MOBIUS TRANSFORMATIONS AND ATTRACTORS ON THE REAL LINE

Let to be an arbitrary point in the complex plane. For each positive i nteger n we choose s(n)(z) to be -5/(1 + z) or -0.5/(1 + z) with equal probability. We introduce the orbit (z(n))(o)(infinity) where z(n) = s(n)(z(n)-1) for n greater than or equal to 1. We prove that with prob ability one the orbit is attracted to the real axis. In the proof, we have to do some calculations on a computer.