arXiv subjects

Ilaria Castellano

Publications and source records attributed to Ilaria Castellano.

20 records · Page 2Linked to original sources

arXiv2017

Topological entropy for locally linearly compact vector spaces

In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study the fundamental properties of this entropy and we prove the Addition Theorem, showing that the topological entropy is additive with respect to short exact sequences. By means of Lefschetz Duality, we connect the topological entropy to the algebraic entropy in a Bridge Theorem.

math.GR↗

arXiv2016

Algebraic entropy in locally linearly compact vector spaces

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.

math.DS↗