One-Dimensional Dynamics
Publisher: Springer; Brand: Springer
Published: Dec 16, 2011
Format: paperback
Number of pages: 620
ISBN-13: 9783642780455
Description: This monograph gives an account of the state of the art in one-dimensional dynamical systems. It presents the theory in a unified way emphasizing the similarities and differences between invertible and non-invertible dynamics (i.e., between diffeomorphisms and endomorphisms).It starts with the invertible case: the combinatorial topological, ergodic and smooth structures are analysed extensively. Then it proceeds by showing that endomorphisms have a much richer dynamics, but that the theory for these endomorphisms can still be developed along the same lines and with similar tools. Moreover, holomorphic dynamical systems are shown to be based on similar principles. In fact, it is shown that complex analytic tools are very powerful even for the study of real one-dimensional systems. 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.
Notes: Source title: One-Dimensional Dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics)