It is a general problem to find appropriate sets of moduli for families of functions that generate dynamical systems. In this paper we solve this problem for a specific family of holomorphic self-maps of ℂ* defined by
The main theorem states that any function topologically conjugate to a member of ℱ is holomorphically conjugate to some member of the family. It follows that the coefficients of the polynomials P(z) and Q(z) are a suitable set of moduli for the families of dynamical systems generated by these functions.
The moduli spaces of functions in ℱ are easy to study computationally and have been studied by many authors. (See references in the text.)
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