Decompositions of factor codes and embeddings between shift spaces with unequal entropies

Details Decompositions of factor codes and embeddings between shift spaces with unequal entropies Decompositions of factor codes and embeddings between shift spaces with unequal entropies

2012-01-03

arxiv.org/abs/1201.0700v2

Mathematics

Dynamical Systems

14pages, 2 figures; v2) minor revision. to appear in Ergodic Theory Dynamical Systems

Scientific paper

Given a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval from the entropy of Y to that of X. Furthermore, if X is of finite type, we can choose those intermediate subshifts as shifts of finite type. In the second part of the paper, given an embedding from a shift space to an irreducible sofic shift, we characterize the set of the entropies of the intermediate subshifts arising from the decompositions of the given embedding into embeddings.

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