On the quasisymmetrical classification of infinitely renormalizable maps: II. remarks on maps with a bounded type topology.

We use the upper and lower potential functions and Bowen's formula estimating the Hausdorff dimension of the limit set of a regular semigroup generated by finitely many $C^{1+α}$-contracting mappings. This result is an application of the geometric distortion lemma in the first paper at this series.

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