Let $T_2$ and $T_3$ be the $/times 2$ and $/times 3$ transformations on the unit interval $[0,1]$ respectively. We study the points whose orbits under these two dynamical systems approach given points simultaneously. Precisely, for some positive functions $/varphi, /psi : /mathbb{N} /rightarrow /mathbb{R}_+$, for any $y_1, y_2/in [0,1]$, the Lebesgue measure and Hausdorff dimensions of the set                /{x/in [0, 1): |T_2^n x-y_1|</varphi(n), |T_3^n x-y_2|</psi(n) for infinitely many n/}are determined. This is a joint work with Lingmin Liao, Sanju Velani and Evgeniy Zorin.

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