Minimal non-invertible transformations of solenoids
Volume 127 / 2012
Colloquium Mathematicum 127 (2012), 243-252
MSC: Primary 37B05; Secondary 54H20.
DOI: 10.4064/cm127-2-7
Abstract
We construct a continuous non-invertible minimal transformation of an arbitrary solenoid. Since solenoids, as all other compact monothetic groups, also admit minimal homeomorphisms, our result allows one to classify solenoids among continua admitting both invertible and non-invertible continuous minimal maps.
