The "spectral" decomposition for one-dimensional maps
Dynamical Systems
2016-01-25 v1
Abstract
We construct the "spectral" decomposition of the sets , and for a continuous map of the interval to itself. Several corollaries are obtained; the main ones describe the generic properties of -invariant measures, the structure of the set 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.
Keywords
Cite
@article{arxiv.math/9201290,
title = {The "spectral" decomposition for one-dimensional maps},
author = {Alexander M. Blokh},
journal= {arXiv preprint arXiv:math/9201290},
year = {2016}
}