Dynamics in One Dimension
Dynamics in One Dimension
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DOI：
10.1007/bfb0084762
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发表时间：
1992-03
期刊：
影响因子：
--
通讯作者：
Louis Block;W. A. Coppel
中科院分区：
文献类型：
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作者：
Louis Block;W. A. Coppel
区间单峰映射（如Logistic映射）在迭代下的行为最近引起了相当大的关注。对于区间上的任意连续映射，迄今为止已经建立了一个实质性的理论，这一点并不广为人知。这本书的目的是给一个明确的帐户，这一主题，与完整的证明，许多强大的，一般性质。在一些情况下，这些信息以前很难获得。本文还对圆的映射的类似理论进行了综述。虽然大部分的结果是未知的三十年前，这本书将是理解的任何人谁掌握了第一门课程，在真实的分析。因此，这本书将是有用的，不仅对学生和研究人员，但也将提供数学家一般的理解如何简单的系统可以表现出混乱的行为。
The behaviour under iteration of unimodal maps of an interval, such as the logistic map, has recently attracted considerable attention. It is not so widely known that a substantial theory has by now been built up for arbitrary continuous maps of an interval. The purpose of the book is to give a clear account of this subject, with complete proofs of many strong, general properties. In a number of cases these have previously been difficult of access. The analogous theory for maps of a circle is also surveyed. Although most of the results were unknown thirty years ago, the book will be intelligible to anyone who has mastered a first course in real analysis. Thus the book will be of use not only to students and researchers, but will also provide mathematicians generally with an understanding of how simple systems can exhibit chaotic behaviour.