On the escape rate of subshifts of finite type and 2-multiplicative integer systems on ${\mathbb{N}}^d$

Abstract

In this article, we establish the escape rate formula for an ${\mathbb{N}}^d$ subshift of finite type $X$ by means of the horizontal transition matrices of the strip shifts induced from $X$. This extends the previous result of Haritha and Agarwal (2019) to ${\mathbb{N}}^d$, $d\ge 1$. The concept of the escape rate for ${\mathbb{N}}^d$ 2-multiplicative integer systems is also introduced, and we give a similar result for the estimate of the escape rate for such systems. Finally, the continuity property for both systems is presented.