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arXiv · 2604.13189

The interplay between partial specification, average shadowing, and Besicovitch completeness

Melih Emin Can·Marcin Kulczycki
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Abstract

Let $(X,T)$ be a compact dynamical system. This article proves that if $(X,T)$ has the partial specification property, then it has the average shadowing property. It is also proven that if $(X,T)$ is surjective and has the partial specification property, then the set of ergodic measures of $(X,T)$ is dense in the space of its invariant measures. An example of a compact dynamical system that is not Besicovitch complete is also given.

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Melih Emin Can, Marcin Kulczycki. 2026-04-14. The interplay between partial specification, average shadowing, and Besicovitch completeness. https://arxiv.org/abs/2604.13189

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