METRIC RESULTS FOR THE EVENTUALLY ALWAYS HITTING POINTS AND LEVEL SETS IN SUBSHIFT WITH SPECIFICATION

Bo Wang () and Bing Li
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Bo Wang: Department of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China
Bing Li: Department of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 06, 1-23

Abstract: We study the set of eventually always hitting points for symbolic dynamics with specification. The measure and Hausdorff dimension of such fractal set are obtained. Moreover, we establish the stronger metric results by introducing a new quantity LN(ω) which describes the maximal length of string of zeros 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.

Keywords: Eventually Always Hitting Points; Subshift; Specification; Fractal Sets; Hausdorff Dimension; Ruelle Operator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24501184

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