Tootfinder

This https://arxiv.org/abs/2208.01989 has been replaced.
link: https://scholar.google.com/scholar?q=a

Thermodynamic Formalism on the Skorokhod space: the continuous time Ruelle operator, entropy, pressure, entropy production and expansiveness
Consider the semi-flow given by the continuous time shift $Θ_t:\mathcal{D} \to \mathcal{D} $, $t \geq 0$, acting on the $\mathcal{D} $ of \textit{càdlàg} paths $w: [0,\infty) \to S^1$, where $S^1$ is the unitary circle. We equip the space $\mathcal{D} $ with the Skorokhod metric, and we show that the semi-flow is expanding. We also introduce a stochastic semi-group $e^{t\, L}$, $t \geq 0,$ where $L$ acts linearly on continuous functions $f:S^1\to\mathbb{R}$. This stochastic semigroup and a…

This https://arxiv.org/abs/2304.03685 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Horseshoes for a class of nonuniformly expanding random dynamical systems on the circle
We propose a notion of random horseshoe for one-dimensional random dynamical systems. We prove the abundance of random horseshoes for a class of circle endomorphisms subject to additive noise, large enough to make the Lyapunov exponent positive. In particular, we provide conditions which guarantee that given any pair of disjoint intervals, for almost every noise realization, there exists a positive density sequence of return times to these intervals such that the induced dynamics are the full s…

This https://arxiv.org/abs/2303.16345 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

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