Ergodic Theory and Differentiable Dynamics
Ergodic Theory and Differentiable Dynamics
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DOI：
10.1007/978-3-642-70335-5
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发表时间：
1986-12
期刊：
影响因子：
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通讯作者：
R. Mãné
中科院分区：
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作者：
R. Mãné
这个版本不同于葡萄牙语版只有在一些补充和许多小的更正。当然，这个版本提出了是否利用这个机会引入重大补充的问题。在这样一本书中，结束于一个丰富的研究领域的核心，总是有更进一步的主题，可以说应该包括在内。像测地线流或豪斯多夫维数在当代遍历理论中的作用这样的主题是两个最诱人的空白。然而，我让它站在几乎相同的边界作为原来的版本，仍然相信这些充分满足其目标，提出所需的基本知识，以接近研究领域的微分遍历理论。我想感谢利维博士出色的翻译和上面提到的几个更正。里约热内卢，1987年1月里卡多马内介绍这本书是一个介绍遍历理论，重点是它的关系与理论的微分动力系统，这有时被称为微分遍历理论。第0章，测度理论的快速回顾，包括作为参考。证明被省略，除了一些结果的衍生品方面的序列的分区，这是不一般发现在标准文本的措施和整合理论，往往是失去了一个更广泛的框架内，更先进的文本。
This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.