Entropy for Symbolic Dynamics with Overlapping Alphabets
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.
KeywordsSymbolic dynamics Topological entropy Subshifts of finite type Non-unique itineraries
Mathematics Subject ClassificationPrimary 37B10 37B40 Secondary 37B30 37D05 37C15
Jim Wiseman was supported by the Holder Fund for Faculty Innovation.
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