Topological entropy for locally linearly compact vector spaces and field extensions

TL;DR

This paper develops formulas to compute the topological entropy of flows over locally linearly compact vector spaces when changing the base field via extension or restriction of scalars.

Contribution

It introduces explicit formulas for topological entropy calculations in the context of scalar extension and restriction for locally linearly compact vector spaces.

Findings

Formulas for entropy under scalar extension

Formulas for entropy under scalar restriction

Application to flows over locally linearly compact spaces

Abstract

Let $\mathbb{K}$ be a discrete field and $(V, \phi)$ a flow over the category of locally linearly compact $\mathbb{K}$-spaces. Here we give the formulas to compute the topological entropy of $(V,\phi)$ subject to the extension or the restriction of scalars.