Endomorphisms of Sturmian systems and the discrete chair substitution tiling system
Jeanette Olli · Discrete and Continuous Dynamical Systems · 2013
When looking at a dynamical system, a natural question to ask is what are its endomorphisms. Using Coven's work in [1] on the endomorphisms of dynamical systems generated by substitutions of equal length on {0,1} as a guide, we fully describe the endomorphisms for a class of almost automorphic symbolic dynamical systems provided there are certain conditions on the set where the factor map fails to be 1-1. While this result does have conditions on both the dynamical system and the factor map, it applies to Sturmian systems and generalized Sturmian systems. We also prove a similar result for a particular 2-dimensional system with a $\mathbb{Z}^2$-action, the discrete chair substitution tiling system.