  For an ergodic hyperbolic measure $\omega$ of a $C^{1+{\alpha}}$
diffeomorphism, there is an $\omega$ full-measured set $\tilde\Lambda$ such
that every nonempty, compact and connected subset $V$ of
$\mathbb{M}_{inv}(\tilde\Lambda)$ coincides with the accumulating set of time
averages of Dirac measures supported at {\it one orbit}, where
$\mathbb{M}_{inv}(\tilde\Lambda)$ denotes the space of invariant measures
supported on $\tilde\Lambda$. Such state points corresponding to a fixed $V$
are dense in the support $supp(\omega)$. Moreover,
$\mathbb{M}_{inv}(\tilde\Lambda)$ can be accumulated by time averages of Dirac
measures supported at {\it one orbit}, and such state points form a residual
subset of $supp(\omega)$. These extend results of Sigmund [9] from uniformly
hyperbolic case to non-uniformly hyperbolic case. As a corollary, irregular
points form a residual set of $supp(\omega)$.
