2007/03/19 by J. H. Lowenstein, F. Vivaldi, Lowenstein, J. H. +1
Mathematics · #11Z05 #37E05 #37E20 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11Z05 #msc:37E05 #msc:37E20
paper · pdf · doi:10.48550/arxiv.math/0703556
18 pages
arxiv created 2007/03/19 · arxiv updated 2009/12/01
We study the dynamics of renormalisation of an interval exchange transformation which features exact scaling (the cubic Arnoux-Yoccoz model). Using a symbolic space that describes both dynamics and scaling, we characterize the periodic points of the scaling map in terms of generalised decimal expansions, where the base is the reciprocal of a Pisot number and the digits are algebraic integers. We establish rigorously some basic facts, and use extensive numerical experimentation to formulate a conjecture.