Dynamics Seminar

Event Information Self-induced rectangle exchange maps
15:10 on Monday February 05, 2018
16:00 on Monday February 05, 2018
BA6183, Bahen Center, 40 St. George St.
Ren Yi

Brown University

Rectangle exchange maps (REMs) are higher dimensional generalizations of interval exchange maps which have been well-studied for more than fourty years. We study REMs that arise from cut-and-project schemes on lattices associated to cubic Pisot numbers. We prove that these REMs are minimal and self-induced. Moreover, these REMs are parametrized by matrices in SL(7,Z) whose leading non-zero eigenvalues are Pisot numbers. Via matrix products, we identify a family of renormalizable REMs whose parameter space is a four-dimensional Cantor set. We will give a symbolic encoding of the dynamical system on the parameter space. This is joint work with Ian Alevy and Richard Kenyon.