Scale Recurrence Lemma and Dimension Formula for Cantor Sets in the Complex Plane
Abstract
We will prove a multidimensional conformal version of the scale recurrence lemma of Moreira and Yoccoz MY for Cantor sets in the complex plane. We then use this new recurrence lemma, together with the ideas in M, to prove that under the right hypothesis for the Cantor sets K1,...,Kn and the function h:Cn Rl, the following formula holds \[HD(h(K1× K2 × ...× Kn))= \l,HD(K1)+...+HD(Kn)\.\]
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