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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.14462 |
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| _version_ | 1866916582061506560 |
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| author | Talebi, Amin |
| author_facet | Talebi, Amin |
| contents | \textit{Non-statistical dynamics} are those for which a set of points with positive measure (w.r.t. a reference probability measure which is in most examples the Lebesgue on a manifold) do not have a convergent sequence of empirical measures. In this paper, we show that behind the existence of non-statistical dynamics, there is some other dynamical property: \textit{statistical instability}. To this aim, we present a general formalization of the notions of statistical stability and instability and introduce sufficient conditions on a subset of dynamical systems to contain non-statistical maps in terms of statistical instability. We follow this idea and introduce a new class of non-statistical maps in the space of Anasov-Katok diffeomorphisms of the annulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_14462 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Non-statistical behavior via Statistical instability: Non-statistical Anosov-Katok diffeomorphisms Talebi, Amin Dynamical Systems \textit{Non-statistical dynamics} are those for which a set of points with positive measure (w.r.t. a reference probability measure which is in most examples the Lebesgue on a manifold) do not have a convergent sequence of empirical measures. In this paper, we show that behind the existence of non-statistical dynamics, there is some other dynamical property: \textit{statistical instability}. To this aim, we present a general formalization of the notions of statistical stability and instability and introduce sufficient conditions on a subset of dynamical systems to contain non-statistical maps in terms of statistical instability. We follow this idea and introduce a new class of non-statistical maps in the space of Anasov-Katok diffeomorphisms of the annulus. |
| title | Non-statistical behavior via Statistical instability: Non-statistical Anosov-Katok diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2012.14462 |