On Ilyashenko's Statistical Attractors
Dynamical Systems
2014-02-04 v4
Abstract
We define a minimal alpha-observability of Ilyashenko's statistical attractors. We prove that the space is always full Lebesgue decomposable into pairwise disjoint sets that are Lebesgue-bounded away from zero and included in the basins of a finite family of minimal alpha-observable statistical attractors. Among other examples, we analyze the Bowen homeomorphisms with non robust topological heteroclinic cycles. We prove the existence of three types of statistical behaviours for these examples.
Keywords
Cite
@article{arxiv.1106.4072,
title = {On Ilyashenko's Statistical Attractors},
author = {Eleonora Catsigeras},
journal= {arXiv preprint arXiv:1106.4072},
year = {2014}
}
Comments
This version has changes suggested by the anonymous referee. Accepted for publication in "Dynamical Systems - An International Journal". The final version will appear in http://www.tandfonline.com/toc/cdss20/current#.UikiPX96-ME