On the ergodic theory of free group actions by real-analytic circle diffeomorphisms

被引：6

作者：

Deroin, Bertrand ^{[1
,2
]}

Kleptsyn, Victor ^{[3
,4
]}

Navas, Andres ^{[5
]}

机构：

[1] Univ Cergy Pontoise, CNRS, 2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise, France

[2] Univ Cergy Pontoise, Dept Math AGM, 2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise, France

[3] Univ Rennes 1, CNRS, Bat 22-23,Campus Beaulieu, F-35042 Rennes, France

[4] Univ Rennes 1, Inst Rech Math Rennes, UMR 6625, Bat 22-23,Campus Beaulieu, F-35042 Rennes, France

[5] Univ Santiago Chile, Estn Cent, Alameda 3363, Santiago, Chile

来源：

INVENTIONES MATHEMATICAE | 2018年 / 212卷 / 03期

关键词：

FOLIATIONS; SUBGROUPS;

D O I：

10.1007/s00222-017-0779-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are only finitely many orbits of connected components of its complement. For the case of minimal actions, we show that if the underlying group is (algebraically) free, then the action is ergodic with respect to the Lebesgue measure. This provides first answers to questions due to Ae. Ghys, G. Hector and D. Sullivan.

引用

页码：731 / 779

页数：49

共 47 条

[1] On the ergodic theory of free group actions by real-analytic circle diffeomorphisms
Bertrand Deroin
Victor Kleptsyn
Andrés Navas
[J]. Inventiones mathematicae, 2018, 212 : 731 - 779
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[J]. STUDIA MATHEMATICA, 2015, 229 (02) : 141 - 172
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[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2017, 37 : 1547 - 1569
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