The "spectral" decomposition for one-dimensional maps

Details The "spectral" decomposition for one-dimensional maps The "spectral" decomposition for one-dimensional maps

1991-07-27

arxiv.org/abs/math/9201290v1

Dynamics Reported 4(1995), 1-59

Mathematics

Dynamical Systems

Scientific paper

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.

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