  In 1995, Hill and Velani introduced the shrinking targets theory. Given a
dynamical system $([0,1],T)$, they investigated the Hausdorff dimension of sets
of points whose orbits are close to some fixed point. In this paper, we study
the sets of points well-approximated by orbits $\{T^n x\}_{n\geq 0}$, where $T$
is an expanding Markov map with a finite partition supported by $[0,1]$. The
dimensions of these sets are described using the multifractal properties of
invariant Gibbs measures.
