منابع مشابه
Independence entropy of Zd-shift spaces
We introduce a concept of independence entropy for symbolic dynamical systems. This notion of entropy measures the extent to which one can freely insert symbols in positions without violating the constraint defined by the shift space. We show that for a certain class of one-dimensional shift spaces X, the independence entropy coincides with the limiting, as d tends to infinity, topological entr...
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Topological entropy is the most fundamental numerical invariant associated to a d-dimensional shift space. When d = 1 and the shift space is a shift of finite type (SFT) or sofic shift, the topological entropy is easy to compute as the log of the largest eigenvalue of a nonnegative integer matrix. However, when d = 2 there is no known explicit expression for the topological entropy of SFTs, eve...
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For a (compact) subset K of a metric space and ε > 0, the covering number N(K, ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In t...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2018
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2018.1401875