  For a simple model of chaotic dynamical systems with a large number of
degrees of freedom, we find that there is an ensemble of unstable periodic
orbits (UPOs) with the special property that the expectation values of
macroscopic quantities can be calculated using only one UPO sampled from the
ensemble. Evidence to support this conclusion is obtained by generating the
ensemble by Monte Carlo calculation for a statistical mechanical model
described by a space-time Hamiltonian that is expressed in terms of Floquet
exponents of UPOs. This result allows us to interpret the recent interesting
discovery that statistical properties of turbulence can be obtained from only
one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato
and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].
