Diophantine approximation and special Liouville numbers

This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers ${\zeta }_1,{\zeta }_2,\mathrm{.}\mathrm{.}\mathrm{.},{\zeta }_k$. The approach relies on results on the connection between the set of all $s$-adic expansions ($s\ge 2$) of ${\zeta }_1,{\zeta }_2,\mathrm{.}\mathrm{.}\mathrm{.},{\zeta }_k$ and their associated approximation constants. As an application, explicit construction of real numbers ${\zeta }_1,{\zeta }_2,\mathrm{.}\mathrm{.}\mathrm{.},{\zeta }_k$ with prescribed approximation properties are deduced and illustrated by Matlab plots.