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arXiv · 1106.4072

On Ilyashenko's Statistical Attractors

Eleonora Catsigeras
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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.

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Eleonora Catsigeras. 2013-09-06. On Ilyashenko's Statistical Attractors. https://doi.org/10.1080/14689367.2013.843644

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