One-Dimensional Dynamics

This monograph gives an account of the state of the art in one-dimensional dynamical systems. The subject is studied from a combinatorial, continuous, ergodic and smooth point of view. Several results in this book are new; moreover, the exciting new developments on universality and renormalization due to D. Sullivan, are presented here in full detail for the first time. The results are presented in a unified way and with complete and thorough proofs. The study of circle maps, interval and holomorphic maps of the Riemann sphere are all shown to be based on similar principles. With this book, the reader is able to quickly get to the frontier of this exciting subject without studying many inaccessible papers.