TY - JOUR
T1 - On the ergodic theory of free group actions by real-analytic circle diffeomorphisms
AU - Deroin, Bertrand
AU - Kleptsyn, Victor
AU - Navas, Andrés
N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - 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 É. Ghys, G. Hector and D. Sullivan.
AB - 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 É. Ghys, G. Hector and D. Sullivan.
U2 - 10.1007/s00222-017-0779-4
DO - 10.1007/s00222-017-0779-4
M3 - Article
AN - SCOPUS:85038356632
SN - 0020-9910
VL - 212
SP - 731
EP - 779
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -