RT Journal Article
T1 Wild Cantor actions
A1 Lukina, Olga
A1 Nozawa, Hiraku
A1 Álvarez López, Jesús Antonio
A1 Barral Lijó, Ramón
K1 Cantor sets
K1 Centralizer direct limit group
K1 Equicontinuous actions
K1 Group actions
K1 Group actions on rooted trees
K1 Profinite groups
K1 Stabilizer direct limit group
K1 The alternating group
K1 The cyclic group
K1 Wreath products
AB The discriminant group of a minimal equicontinuous action of a group $G$ on a Cantor set $X$ is the subgroup of the closure of the action in the group of homeomorphisms of $X$, consisting of homeomorphisms which fix a given point. The stabilizer and the centralizer groups associated to the action are obtained as direct limits of sequences of subgroups of the discriminant group with certain properties. Minimal equicontinuous group actions on Cantor sets admit a classification by the properties of the stabilizer and centralizer direct limit groups.In this paper, we construct new families of examples of minimal equicontinuous actions on Cantor sets, which illustrate certain aspects of this classification. These examples are constructed as actions on rooted trees. The acting groups are countable subgroups of the product or of the wreath product of groups. We discuss applications of our results to the study of attractors of dynamical systems and of minimal sets of foliations.
PB Mathematical Society of Japan
YR 2022
FD 2022-04
LK http://hdl.handle.net/10347/32123
UL http://hdl.handle.net/10347/32123
LA eng
NO Álvarez López, J.A., Barral Lijó, R., Lukina, O., Nozawa, H. (2022). Wild Cantor actions. "J. Math. Soc. Japan", vol. 74, 447-472.
NO Project MTM2017-89686-P (AEI/FEDER, UE) [JAL]; Canon Foundation in Europe Research Fellowship [RBL]; FWF Project P31950-N35 [OL]; JSPS KAKENHI Grant number 17K14195 and 20K03620 [HN].
DS Minerva
RD 24 abr 2026