Poincare recurrences of DNA sequences

We analyze the statistical properties of Poincare recurrences of Homo sapiens, mammalian, and other DNA sequences taken from the Ensembl Genome data base with up to 15 billion base pairs. We show that the probability of Poincare recurrences decays in an algebraic way with the Poincare exponent beta approximate to 4 even if the oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent nu approximate to 0.6 that leads to an anomalous superdiffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than one million base pairs. We argue that the approach based on Poncare recurrences determines new proximity features between different species and sheds a new light on their evolution history.