Compositions of Random Möbius Transformations

Abstract

Let be a sequence of i.i.d. random variables taking values in the set of all Möbius transformations. Consider the sequence defined by where z belongs to the extended complex plane. Necessary and sufficient conditions for a.s. convergence of will be discussed. As an application we will see how a sequence of the form may be used to generalize a mathematical model of phyllotaxis. Some results concerning the convergence in distribution of will also be discussed.

Key Words:

• Random Möbius transformations
• Phyllotaxis
• Cut-grow model