Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale Recurrence Lemma and Dimension Formula for Cantor Sets in the
  Complex Plane   We will prove a multidimensional conformal version of the scale recurrence
lemma of Moreira and Yoccoz \cite{MY} for Cantor sets in the complex plane. We
then use this new recurrence lemma, together with the ideas in \cite{M}, to
prove that under the right hypothesis for the Cantor sets $K_1,...,K_n$ and the
function $h:\mathbb{C}^{n}\to \mathbb{R}^{l}$, the following formula holds
\[HD(h(K_1\times K_2 \times ...\times K_n))=\min \{l,HD(K_1)+...+HD(K_n)\}.\]

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph