Algebraic entropy in locally linearly compact vector spaces

TL;DR

This paper extends the concept of algebraic entropy to continuous endomorphisms of locally linearly compact vector spaces, preserving key properties like the Addition Theorem, thus broadening its applicability in topological vector space dynamics.

Contribution

It introduces algebraic entropy for locally linearly compact vector spaces and proves that fundamental properties, including the Addition Theorem, still hold in this broader setting.

Findings

Algebraic entropy defined for continuous endomorphisms in this context.

Main properties of entropy, including the Addition Theorem, are extended.

The framework generalizes entropy concepts from discrete to locally linearly compact spaces.

Abstract

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the main properties of entropy continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem.