Torsion groups from minimal actions of the infinite dihedral group

We will show how minimal actions of the infinite dihedral group can be used to construct finitely generated infinite torsion groups. For instance, we will describe a family of torsion groups constructed from the actions generated by reflections of the circle with respect to two diameters with an irrational angle between them. If the angle is an irrational number of bounded type, then the associated group is of subexponential growth. Some open problems will be formulated.