Abstract
AbstractLet 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.
Highlights
An entropy function over a category C can be regarded as an invariant h : Flow(C) → N ∪ {∞}, of the category Flow(C), whose objects are the ows de ned over C
We provide the formulae to compute the topological entropy ent* of the ow (V, φ) subject to either extension or restriction of scalars
The rst appearance of topological entropy was in 1965 when Adler, Konheim and McAndrew [1] de ned it for continuous self-maps of compact spaces
Summary
An entropy function over a category C can be regarded as an invariant h : Flow(C) → N ∪ {∞}, of the category Flow(C), whose objects are the ows de ned over C. For a nite eld K, every locally linearly compact K-space V is a totally disconnected locally compact abelian group and htop(V , φ) = ent*(V , φ) · log |K|, for every continuous endomorphism φ : V → V (see [6, Proposition 3.9]). In the latter equation it is clear that the size of the eld K a ects - as predictable - the value of the topological entropy. This paper is intended to be a complement to [5, 6] where ent* for locally linearly compact K-spaces has been introduced and studied
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