Lukina, OlgaNozawa, HirakuÁlvarez López, Jesús AntonioBarral Lijó, Ramón2024-01-312024-01-312022-04Álvarez López, J.A., Barral Lijó, R., Lukina, O., Nozawa, H. (2022). Wild Cantor actions. "J. Math. Soc. Japan", vol. 74, 447-472.http://hdl.handle.net/10347/32123The 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Cantor setsCentralizer direct limit groupEquicontinuous actionsGroup actionsGroup actions on rooted treesProfinite groupsStabilizer direct limit groupThe alternating groupThe cyclic groupWreath products110206 Fundamentos de matemáticasjournal article10.2969/jmsj/85748574open access