Metric results for the eventually always hitting points and level sets in subshift with specification
Abstract
We study the set of eventually always hitting points for symbolic dynamics with specification. The measure and Hausdorff dimension of such sets are obtained. Moreover, we establish the stronger metric results by introducing a new quantity LN(ω) which describes the maximal length of string of zreos of the prefix among the first N iterations of ω in symbolic space. The Hausdorff dimensions of the level sets for this quantity are also completely determined.
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