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 {Tnx}n≥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.Comment: 24 pages, 3 figures; To appear in ETDS, 201