Hausdorff dimension of the recurrence set of Gauss transformation

Let x₀ ? [0,1){x_0in [0,1)} be an irrational number and {t _n } _n≥1 be a nondecreasing sequence of natural numbers. The recurrence set of Gauss transformation T is defined by

E(x0)={x ? [0,1):Tn(x) ? Itn(x0) for infinitely many n},E(x_0)={xin[0,1):T^n(x)in I_{t_n}(x_0) for infinitely many n},
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