Entropy for Symbolic Dynamics with Overlapping Alphabets
Student author: Fabio Drucker
Journal of Dynamics and Differential Equations
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces and show that it is equal to a limit of entropies of standard (non-overlapping) shifts when the underlying shift is of finite type. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.
Drucker, Fabio, David Richeson, and Jim Wiseman. "Entropy for Symbolic Dynamics with Overlapping Alphabets." Journal of Dynamics and Differential Equations 28 (2016): 301-315. https://link.springer.com/article/10.1007/s10884-016-9535-5