On the question of ergodicity for minimal group actions on the circle
On the question of ergodicity for minimal group actions on the circle
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DOI：
10.17323/1609-4514-2009-9-2-263-303
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发表时间：
2008-06
期刊：
影响因子：
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通讯作者：
B. Deroin;V. Kleptsyn;A. Navas
中科院分区：
文献类型：
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作者：
B. Deroin;V. Kleptsyn;A. Navas
本文主要研究环上的极小光滑作用群。我们提供了一个充分条件，这样的行动是遍历（关于勒贝格措施），我们说明了这个条件，通过研究两个相关的例子。在一个类似的假设下，我们也处理例外极小集的零Lebesgue测度的问题。这个假设导致了许多其他有趣的结论，主要是关于固定和共形措施。此外，还有几个问题有待解决。这些方法也适用于余维一叶理，尽管这种情况下的结果没有明确说明。
This work is devoted to the study of minimal, smooth actions of finitely generated groups on the circle. We provide a sufficient condition for such an action to be ergodic (with respect to the Lebesgue measure), and we illustrate this condition by studying two relevant examples. Under an analogous hypothesis, we also deal with the problem of the zero Lebesgue measure for exceptional minimal sets. This hypothesis leads to many other interesting conclusions, mainly concerning the stationary and conformal measures. Moreover, several questions are left open. The methods work as well for codimension-one foliations, though the results for this case are not explicitly stated.