  We analyze the statistical properties of Poincar\'e recurrences of Homo
sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base
with up to fifteen billions base pairs. We show that the probability of
Poincar\'e recurrences decays in an algebraic way with the Poincar\'e exponent
$\beta \approx 4$ even if oscillatory dependence is well pronounced. The
correlations between recurrences decay with an exponent $\nu \approx 0.6$ that
leads to an anomalous super-diffusive walk. However, for Homo sapiens
sequences, with the largest available statistics, the diffusion coefficient
converges to a finite value on distances larger than million base pairs. We
argue that the approach based on Poncar\'e recurrences determines new proximity
features between different species and shed a new light on their evolution
history.
