We construct the "spectral" decomposition of the sets $\bar{Per\,f}$,
$\omega(f)=\cup\omega(x)$ and $\Omega(f)$ for a continuous map $f$ of the
interval to itself. Several corollaries are obtained; the main ones describe
the generic properties of $f$-invariant measures, the structure of the set
$\Omega(f)\setminus \bar{Per\,f}$ and the generic limit behavior of an orbit
for maps without wandering intervals. The "spectral" decomposition for
piecewise-monotone maps is deduced from the Decomposition Theorem. Finally we
explain how to extend the results of the present paper for a continuous map of
a one-dimensional branched manifold into itself.
