| Higher-Dimensional Subshifts of Finite Type, Factor Maps and Measures of Maximal Entropy (2001) | |||||||||||||||
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| We investigate factor maps of higher-dimensional subshifts of finite type. First we give higher-dimensional versions of well known one-dimensional results, including a characterization of entropy-preserving factor maps. Next, we investigate what happens to the number of measures of maximal entropy under factor maps. We show that this number is preserved under almost invertible maps, but not in general under finite to one factor maps. 1 Introduction In this paper we discuss some aspects of higher-dimensional subshifts of finite type. The book of Lind and Marcus ([4]) is an excellent introduction to the theory of onedimensional symbolic dynamics. It turns out however, as is well known, that the higherdimensional theory is different from the one-dimensional theory. Many one-dimensional results are simply not true in higher dimensions. In addition, in higher dimensions, new concepts arise that do not have one-dimensional analogues. In this paper we address issues of both types. For an exa... | |||||||||||||||
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