$k$-type entropy of ${\mathbb{Z}}^d$ actions

Abstract

We introduce the concept of \(k\)-type entropy for dynamical systems generated by \(\mathbb{Z}^d\)-actions on compact metric spaces. We investigate its fundamental properties and establish connections with classical entropy and other \(k\)-type dynamical notions. The $k$-type entropy of some ${\mathbb{Z}}^2$-actions on a two dimensional torus is also calculated.