## Institute for Mathematical Sciences

## Preprint ims91-14

** A. M. Blokh**
* The "Spectral" Decomposition for One-Dimensional Maps*

Abstract: We construct the ``spectral'' decomposition of the sets $\overline{Per\,f}$, $\omega(f)=\cup\omega(x)$ 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
$\Omega(f)\setminus \overline{Per\,f}$ 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.

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