Topological entropy for locally linearly compact vector spaces and field extensions

Abstract

Let 𝕂 be a discrete field and (V, ϕ) a pair consisting of a locally linearly compact 𝕂-space V and a continuous endomorphism ϕ: V → V. We provide the formulae to compute the topological entropy ent* of the flow (V, ϕ) subject to either extension or restriction of scalars.

Keywords

• linearly compact vector space
• locally linearly compact vector space
• topological entropy
• continuous endomorphism
• extension
• restriction
• algebraic dynamical system
• 37a35
• 15a03
• 15a04
• 20k30
• 22b05