The Hausdorff dimension of recurrent sets in symbolic spaces
نویسندگان
چکیده
Let ( , σ ) be the one-sided shift space onm symbols. For any x = (xi)i 1 ∈ and positive integer n, define Rn(x) = inf{j n : x1x2 · · · xn = xj+1xj+2 · · · xj+n}. We prove that for each pair of numbersα, β ∈ [0,∞] withα β, the following recurrent set Eα,β = { x ∈ : lim inf n→∞ logRn(x) n = α, lim sup n→∞ logRn(x) n = β } has Hausdorff dimension one. AMS classification scheme number: 28A80
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