2021/03/16 by Ferenczi, Sébastien, Hubert, Pascal · 1 citation
#37B10 #37E30 #37E35 #37F34 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37E05 #Secondary 37A05
paper · doi:10.48550/arxiv.2103.09018
We give conditions for minimality of \mathbb Z/N\mathbb Z extensions of a rotation of angle α with one marked point, solving the problem for any prime N: for N=2, these correspond to the Veech 1969 examples, for which a necessary and sufficient condition was not known yet. We provide also a word combinatorial criterion of minimality valid for general interval exchange transformations, which applies to \mathbb Z/N\mathbb Z extensions of any interval exchange transformation with any number of marked points. Then we give a condition for unique ergodicity of these extensions when the initial interval exchange transformation is linearly recurrent and there are one or two marked points.