测度保持作用的紧族和典型熵不变量

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2021-02-11 DOI:10.1090/mosc/321

V. Ryzhikov

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引用次数: 11

摘要

对于一个紧凑的动作集合，Kushnirenko类型的熵被选择为这样一种方式，它在这个集合上消失，但对于典型的动作取无穷大的值。因此，我们发现典型的保测度变换与有限几何图形的等距重排是不同构的。

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Compact families and typical entropy invariants of measure-preserving actions

For a compact set of actions, an entropy of Kushnirenko type is chosen in such a way that it vanishes on this set but takes infinite values for the typical actions. As a consequence we find that typical measure-preserving transformations are not isomorphic to isometric rearrangements of a finite set of geometric figures.

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.