Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911416743624704 |
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| author | Castro, Matheus M. Tenaglia, Giuseppe |
| author_facet | Castro, Matheus M. Tenaglia, Giuseppe |
| contents | In this paper, we study the random dynamical system $f_ω^n$ generated by a family of maps $\{f_{ω_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{ω_0 \in [-\varepsilon,\varepsilon]},$ $f_{ω_0}(x) = αξ(x+ω_0) +a\ (\mathrm{mod }\ 1),$ where $ξ: \mathbb S^1 \to \mathbb R$ is a non-degenerated map, $a\in [0,1)$, and $α,\varepsilon>0$. Fixing a constant $c\in (0,1)$, we show that for $α$ sufficiently large and for $\varepsilon > α^{-1+c},$ the random dynamical system $f_ω^n$ presents a random Young tower structure and quenched decay of correlations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16345 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps Castro, Matheus M. Tenaglia, Giuseppe Dynamical Systems 37H12, 37H15, 37A25 In this paper, we study the random dynamical system $f_ω^n$ generated by a family of maps $\{f_{ω_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{ω_0 \in [-\varepsilon,\varepsilon]},$ $f_{ω_0}(x) = αξ(x+ω_0) +a\ (\mathrm{mod }\ 1),$ where $ξ: \mathbb S^1 \to \mathbb R$ is a non-degenerated map, $a\in [0,1)$, and $α,\varepsilon>0$. Fixing a constant $c\in (0,1)$, we show that for $α$ sufficiently large and for $\varepsilon > α^{-1+c},$ the random dynamical system $f_ω^n$ presents a random Young tower structure and quenched decay of correlations. |
| title | Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps |
| topic | Dynamical Systems 37H12, 37H15, 37A25 |
| url | https://arxiv.org/abs/2303.16345 |