The "spectral" decomposition for one-dimensional maps
Alexander M. Blokh
Abstract
We construct the "spectral" decomposition of the sets Per\,f, ω(f)=ω(x) and (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 (f) 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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