One-dimensional maps via complex analysis in several variables

In this article we use elements from the theory of several complex variables to establish dynamical properties of certain one-dimensional maps (e.g. decay of correlations, central limit theorems, etc.). I am grateful to David Ruelle for introducing me to the Bochner theorem in September 1984 and for making a copy of his article 15] available to me prior to publication. I would also like to thank S. Krantz, E. Bedford and H. Weiss for advice on the complex analysis and G. Keller for comments on interval maps. The author currently holds a Royal Society University Research Fellowship.