Algebraic Entropy in Locally Linearly Compact Vector Spaces

Ilaria Castellano () and Anna Giordano Bruno ()
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Ilaria Castellano: University of Southampton
Anna Giordano Bruno: Università degli Studi di Udine

A chapter in Rings, Polynomials, and Modules, 2017, pp 103-127 from Springer

Abstract: Abstract We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69–87, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem.

Keywords: Linearly compact vector space; Locally linearly compact vector space; Algebraic entropy; Continuous linear transformation; Continuous endomorphism; Algebraic dynamical system; 15A03; 15A04; 22B05; 20K30; 37A35 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-65874-2_6

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