The interplay between partial specification, average shadowing, and Besicovitch completeness
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914473498902528 |
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| author | Can, Melih Emin Kulczycki, Marcin |
| author_facet | Can, Melih Emin Kulczycki, Marcin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13189 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The interplay between partial specification, average shadowing, and Besicovitch completeness Can, Melih Emin Kulczycki, Marcin Dynamical Systems 37B65, 37B05, 37B10 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. |
| title | The interplay between partial specification, average shadowing, and Besicovitch completeness |
| topic | Dynamical Systems 37B65, 37B05, 37B10 |
| url | https://arxiv.org/abs/2604.13189 |