One-Dimensional Dynamics
One-Dimensional Dynamics
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DOI：
10.1007/978-3-642-78043-1
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
W. D. Melo;S. Strien
中科院分区：
文献类型：
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作者：
W. D. Melo;S. Strien
一维动力学在过去的几十年里已经发展成为一门独立的学科。然而，许多最近的结果是无法访问的，从来没有被放在一起。为此，我们试图对这个问题给出一个统一的解释，并对许多结果给出完整的证明。为了显示什么结果，人们可能会期望，第一章涉及的理论，循环的超同态。其余的书是一个试图发展类似的理论在不可逆的情况下，尽管内在的额外困难。用这种方法，我们试图证明在一维动力学中存在一个统一的理论。通过阅读其中的一章或多章，读者可以很快到达研究的前沿。让我们快速总结一下这本书。第一章讨论了圆同态，并给出了关于M的圆同态的光滑线性化定理的完整证明。赫尔曼，J. - C. Yoccoz和其他人第二章对待揉理论的米尔诺和Thurstonj还包括一个阐述霍夫鲍尔的塔建设和一个结果fuB多峰家庭（这最后一个结果解决了一个问题提出的J.米尔诺）。
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).