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

Abstract

In this paper we consider a smooth flow $(\Lambda ,{\Phi }^t)$ builded from suspending over a (non-invertible topologically mixing) subshift of finite type, and we equip it with an equilibrium measure $\nu$ on $\Lambda .$ 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 $$\nu \left\{x\in \Lambda :\left|\int F\circ {\Phi }^s(x)ds-\int Fd\mu \right|>\epsilon \right\}\le \exp (-Xt+\log t+Y)$$ for $t\gg >1\gg \epsilon >0,$ where $F:\Lambda \to \mathbb{R}$ is smooth. The second theorem gives an explicit lower bound for the asymptotic behaviour of the escape rate of $\nu$ through a small hole.

References in corpus (1)

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