Teich Webinar, Friday, January 21th

-rotation Z-Rauzy induction on the torus and associated Markov partitions

Here is his summary: We will study a two-dimensional symbolic dynamic system given by the encoding of a Z 2-rotation on the two-dimensional torus by a well chosen polygonal partition. Using a two-dimensional notion of Rauzy’s induction, we will demonstrate that the score is self-induced. Therefore, the symbolic dynamic system is auto-similar. We will show that it is also of the finished type and we will deduce that the score is a Markov score for the 2-rotation Z on the torus. The purpose of the talk is to illustrate quietly and by hand in the table the calculation of the Rauzy induction for the 2-rotation Z in the simplest case and associated with the golden number. Details of the method are available here