Statistical properties of mostly expanding fast-slow partially hyperbolic systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911271543111680 |
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| author | De Simoi, Jacopo Fernando, Kasun Fleming-Vázquez, Nicholas |
| author_facet | De Simoi, Jacopo Fernando, Kasun Fleming-Vázquez, Nicholas |
| contents | We consider a class of fast-slow $C^4$ partially hyperbolic systems on $\mathbb{T}^2$ given by $ε$-perturbations of maps $F(x,θ)=(f(x,θ),θ)$ where $f(\cdot,θ)$ are $C^{4}$ expanding maps of the circle. For sufficiently small $ε$ and an open set of perturbations we prove existence and uniqueness of a physical measure and exponential decay of correlations for sufficiently smooth observables with explicit almost optimal bounds on the decay rate. Our result complements previous work by De Simoi and Liverani, which studied the case of mostly contracting centre. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical properties of mostly expanding fast-slow partially hyperbolic systems De Simoi, Jacopo Fernando, Kasun Fleming-Vázquez, Nicholas Dynamical Systems We consider a class of fast-slow $C^4$ partially hyperbolic systems on $\mathbb{T}^2$ given by $ε$-perturbations of maps $F(x,θ)=(f(x,θ),θ)$ where $f(\cdot,θ)$ are $C^{4}$ expanding maps of the circle. For sufficiently small $ε$ and an open set of perturbations we prove existence and uniqueness of a physical measure and exponential decay of correlations for sufficiently smooth observables with explicit almost optimal bounds on the decay rate. Our result complements previous work by De Simoi and Liverani, which studied the case of mostly contracting centre. |
| title | Statistical properties of mostly expanding fast-slow partially hyperbolic systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.13919 |