Abstract

In this talk, we will discuss the intrinsic Diophantine approximation on the triadic Cantor set $\K$, i.e. approximating the points in $\K$ by rational numbers in $\K$, a question posed by K. Mahler. By using another height function of a rational number in $\K$, instead of the usual denominator, a complete metric theory for this variant intrinsic Diophantine approximation is presented which yields to the divergence part of Mahler's problem.