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arXiv · 2303.16345

Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps

Matheus M. Castro·Giuseppe Tenaglia
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Abstract

In this paper, we study the random dynamical system $f_\omega^n$ generated by a family of maps $\{f_{\omega_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{\omega_0 \in [-\varepsilon,\varepsilon]},$ $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\ (\mathrm{mod }\ 1),$ where $\xi: \mathbb S^1 \to \mathbb R$ is a non-degenerated map, $a\in [0,1)$, and $\alpha,\varepsilon>0$. Fixing a constant $c\in (0,1)$, we show that for $\alpha$ sufficiently large and for $\varepsilon > \alpha^{-1+c},$ the random dynamical system $f_\omega^n$ presents a random Young tower structure and quenched decay of correlations.

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Matheus M. Castro, Giuseppe Tenaglia. 2023-03-28. Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps. https://doi.org/10.1088/1361-6544%2Fae3418

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