Exponential mixing for singular skew-products
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929541981667328 |
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| author | Butterley, Oliver |
| author_facet | Butterley, Oliver |
| contents | We study skew-products of the form $(x,u) \mapsto (fx, u + φ(x))$ where $f$ is a non-uniformly expanding map on a manifold $X$ and $φ: X \to \mathbb{S}^1$ is piecewise $\mathcal{C}^1$. If the systems satisfies mild assumptions (in particular singular behaviour of $φ$ is permitted) then we prove that the map mixes exponentially with respect to the unique SRB measure. This extends previous results by allowing singular behaviour in the fibre map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13618 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exponential mixing for singular skew-products Butterley, Oliver Dynamical Systems We study skew-products of the form $(x,u) \mapsto (fx, u + φ(x))$ where $f$ is a non-uniformly expanding map on a manifold $X$ and $φ: X \to \mathbb{S}^1$ is piecewise $\mathcal{C}^1$. If the systems satisfies mild assumptions (in particular singular behaviour of $φ$ is permitted) then we prove that the map mixes exponentially with respect to the unique SRB measure. This extends previous results by allowing singular behaviour in the fibre map. |
| title | Exponential mixing for singular skew-products |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2308.13618 |