Ergodic Theory on Compact Spaces
Ergodic Theory on Compact Spaces
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DOI：
10.1007/bfb0082364
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发表时间：
1976-08
期刊：
影响因子：
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通讯作者：
M. Denker;C. Grillenberger;K. Sigmund
中科院分区：
文献类型：
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作者：
M. Denker;C. Grillenberger;K. Sigmund
遍历理论的初始问题出现在一个可微的框架中：能量流形上的光滑流保持Liouville测度。是庞卡莱首次提出纯粹的测量理论考量。可微论和测度论的遍历理论都得到了极大的发展，特别是自从Kolmogorov定义了熵不变量以来。拓扑遍历理论作为这两个领域之间的中介而发展起来。它涉及连续变换和不变Borel测度，可以追溯到1937年Krylov-Bogoliubov[127]的回忆录。在这一卷中，我们试图给出紧空间上的拓扑遍历理论的概述。为方便起见，假设其下层空间是度量的，变换是同胚的。
The initial problems of ergodic theory arose in a differentiable framework: smooth flows on energy manifolds preserving Liouville measure. It was Poincaré who first introduced purely measure theoretic considerations. Both, differentiable and measure theoretic ergodic theory, developped tremendously, especially since Kolmogorov's definition of the entropy invariant. Topological ergodic theory grew as an intermediary between the two fields. It deals with continuous transformations and invariant Borel measures and can be traced back to a memoir of Krylov-Bogoliubov [127] in 1937. In this volume we try to give a survey of the topological ergodic theory on compact spaces. For convenience, the underlying space is assumed to be metric and the transformation to be a homeomorphism.