One-Dimensional Dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) 1993rd Edition by Welington de Melo (PDF)

Description

One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer’s tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Okay, I have the pdf version of this book. It happens to me that the page 108-141-110 connect to each other. The book simply does not contain page 109. This means that the reader would miss a really important property of the splitting block of kneading invariants. How on the earth Springer you can do this??? This even happens in the real book!!!!! For all the readers, you need to go the De-melo website or something to get the first-draft pdf, which contains the 109 page material.

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