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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.
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42
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- A First Course in Dynamics: with a Panorama of Recent Developments by Boris Hasselblatt on page 306, page 314, and Back Matter
- Global Analysis of Dynamical Systems by H.W Broer on page 447, and Back Matter
- Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour (Encyclopaedia of Mathematical Sciences) (v. 9) by D.V. Anosov in Front Matter
- Cascades and Fields in Perceptual Psychophysics by Robert A. M. Gregson in Back Matter
- Holomorphic Dynamics (Cambridge Studies in Advanced Mathematics) by S. Morosawa in Back Matter
See all 42 books citing this book
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