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We investigate stable intersections of conformal Cantor sets and theirconsequences to dynamical systems. First we define this type of Cantor set andrelate it to horseshoes appearing in automorphisms of $\C^2$. Then we studylimit geometries, objects related to the asymptotic shape of the Cantor sets,to obtain a criterion that guarantees stable intersection between someconfigurations. Finally we show that the Buzzard construction of a Newhouseregion on $Aut(\C^2)$ can be seem as a case of stable intersection of Cantorsets in our sense and give some (not optimal) estimative on how \say{thick}those sets have to be.

Stable Intersections of Conformal Cantor Sets