Ergodic Theory
Ergodic Theory
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DOI：
10.1007/978-1-4615-6927-5
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
I. P. Cornfeld;S. V. Fomin;Ya. G. Sinai
中科院分区：
文献类型：
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作者：
I. P. Cornfeld;S. V. Fomin;Ya. G. Sinai
遍历理论是数学的少数几个分支之一，在过去的二十年里发生了根本性的变化。在此之前，除了少数例外，遍历理论主要处理平均问题和一般的定性问题，而现在它是一个强大的混合方法，用于分析动态系统的统计特性。出于这个原因，问题的遍历理论现在的兴趣不仅是数学家，而且研究工作者在物理，生物，化学等大纲这本书成为明确的我们近十年前，但由于各种原因，其写作需要很长一段时间。我们从一开始就坚持的主要原则是在研究大量具体实例中发展遍历理论的途径和方法。正因为如此，第一部分的书包含了描述各类动力系统，和他们的基本分析的基础上的基本概念遍历，混合，和频谱的动力系统。在这里，如同在许多其他情况下一样，形容词”基本的”与”简单的“不是同义词。第二部分是“抽象遍历理论”。它包括动力系统的直积和斜积的描述，Rohlin-Halmos引理，以及具有连续时间的动力系统的特殊表示理论。相当大的一部分涉及熵。
Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with" simple." Part II is devoted to" abstract ergodic theory." It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.