A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914987586355200 |
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| author | Galatolo, Stefano Faranda, Davide |
| author_facet | Galatolo, Stefano Faranda, Davide |
| contents | We prove that if a nonautonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior) then the time $τ_{r}(x,y)$ needed for a typical point $x$ to enter for the first time in a ball $B(y,r)$ centered in $y$, with small radius \ $r $ scales as the local dimension of the equilibrium measure \ $μ$ at $y$, i.e. $$ \underset{r\rightarrow 0}{\lim }\frac{\log τ_{r}(x,y)}{-\log r}% =d_{μ}(y).$$
We then apply the general result to concrete systems of different kind, showing such a logarithm law for asymptotically authonomous solenoidal maps and mean field coupled expanding maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03241 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems Galatolo, Stefano Faranda, Davide Dynamical Systems Chaotic Dynamics 37C60, 37C30, 37N10 We prove that if a nonautonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior) then the time $τ_{r}(x,y)$ needed for a typical point $x$ to enter for the first time in a ball $B(y,r)$ centered in $y$, with small radius \ $r $ scales as the local dimension of the equilibrium measure \ $μ$ at $y$, i.e. $$ \underset{r\rightarrow 0}{\lim }\frac{\log τ_{r}(x,y)}{-\log r}% =d_{μ}(y).$$ We then apply the general result to concrete systems of different kind, showing such a logarithm law for asymptotically authonomous solenoidal maps and mean field coupled expanding maps. |
| title | A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems |
| topic | Dynamical Systems Chaotic Dynamics 37C60, 37C30, 37N10 |
| url | https://arxiv.org/abs/2404.03241 |