  We study Poincar\'e recurrence from a purely geometrical viewpoint. We prove
that the metric entropy is given by the exponential growth rate of return times
to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss
theorem. Moreover, we show that minimal return times to dynamical balls grow
linearly with respect to its length. Finally, some interesting relations
between recurrence, dimension, entropy and Lyapunov exponents of ergodic
measures are given.
