Local dimensions for Poincare recurrences

Pointwise dimensions and spectra for measures associated with Poincare recurrences are calculated for arbitrary weakly specified subshifts with positive entropy and for the corresponding special flows. It is proved that the Poincare recurrence for a "typical" cylinder is asymptotically its length. Examples are provided which show that this is not true for some systems with zero entropy. Precise formulas for dimensions of measures associated with Poincare recurrences are derived, which are comparable to Young's formula for the Hausdorff dimension of measures and Abramov's formula for the entropy of special flows.