  In the framework of the semiclassical approach the universal spectral
correlations in the Hamiltonian systems with classical chaotic dynamics can be
attributed to the systematic correlations between actions of periodic orbits
which (up to the switch in the momentum direction) pass through approximately
the same points of the phase space. By considering symbolic dynamics of the
system one can introduce a natural ultrametric distance between periodic orbits
and organize them into clusters. Each cluster consists of orbits approaching
closely each other in the phase space. We study the distribution of cluster
sizes for the backer's map in the asymptotic limit of long trajectories. This
problem is equivalent to the one of counting degeneracies in the length
spectrum of the {\it de Bruijn} graphs. Based on this fact, we derive the
probability $\P_k$ that $k$ randomly chosen periodic orbits belong to the same
cluster. Furthermore, we find asymptotic behaviour of the largest cluster size
$|\Cll_{\max}|$ and derive the probability $P(t)$ that a random periodic orbit
belongs to a cluster of the size smaller than $t|\Cll_{\max}|$, $t\in[0,1]$.
