Escape rate for special semi-flows over non-invertible subshifts of finite type

Bratteli-Vershik representations of some one-sided substitution subshifts

We study one-sided substitution subshifts, and how they can be represented using Bratteli-Vershik systems. In particular we focus on minimal recognizable substitutions such that the generated one-sided substitution subshift contains only one non-shift-invertible element (a branch point), and we call these substitutions quasi-invertible. We give an algorithm to check whether a substitution is quasi-invertible, and show that any substitution with a rational Perron value is orbit equivalent to a quasi-invertible substitution. If the quasi-invertible substitution is left proper, then its subshift …

关于带有 Markov 测度的 subshift 的逃逸率

On Escape rate for subshift with Markov measure

本文研究了带有 Markov 测度的有限型 subshift 的逃逸率，通过将柱集并集视为洞，提出了基于矩阵 Hadamard 乘积谱半径和递推关系的两种逃逸率表述，以实现对不同洞逃逸率的比较分析。

Subshifts of Finite Type with a Hole

This paper examines the relationship between the escape rate and the minimal period of the hole. We consider a subshift of finite type on $q$ symbols with a union of $t$ cylinders based at words of identical length $p$ as the hole. The escape rate into the hole relates to the asymptotic behavior of the number of words of fixed length that do not contain the fixed set of (forbidden) words at which the cylinders are based. We explore the relationship between the escape rate and $r(z)$, a rational function of the correlations between the forbidden words. In particular, we prove that there exists …

Pressure and escape rates for random subshifts of finite type

In this work we consider several aspects of the thermodynamic formalism in a randomized setting. Let $X$ be a non-trivial mixing shift of finite type, and let $f : X \to \mathbb{R}$ be a Hölder continuous potential with associated Gibbs measure $μ$. Further, fix a parameter $α\in (0,1)$. For each $n \geq 1$, let $\mathcal{F}_n$ be a random subset of words of length $n$, where each word of length $n$ that appears in $X$ is included in $\mathcal{F}_n$ with probability $1-α$ (and excluded with probability $α$), independently of all other words. Then let $Y_n = Y(\mathcal{F}_n)$ be the random subs…

Local Escape Rates for $ϕ$-mixing Dynamical Systems

We show that dynamical systems with $ϕ$-mixing measures have local escape rates which are exponential with rate $1$ at non-periodic points and equal to the extremal index at periodic points. We apply this result to equilibrium states on subshifts of finite type, expanding interval maps, Gibbs states on conformal repellers and more generally to Young towers and by extension to all systems that can be modeled by a Young tower.

A Large deviation and an escape rate result for special semi-flows

In this paper we consider a smooth flow $(Λ,Φ^t)$ builded from suspending over a (non-invertible topologically mixing) subshift of finite type, and we equip it with an equilibrium measure $ν$ on $Λ.$ The two main theorems are a large deviation and an escape rate result. The first theorem gives an explicit formula for $X>0$ and $Y$ such that $$ν\left\{x\inΛ: \left|\int F\circ Φ^s (x) ds-\int F dμ\right|>ε\right\}\leq \exp(-Xt+\log t+Y)$$ for $t\gg>1\ggε>0,$ where $F:Λ\to\mathbb{R}$ is smooth. The second theorem gives an explicit lower bound for the asymptotic behaviour of the escape rate of $ν$…