Abstract
We introduce a modified version of the entropy defined for locally compact Abelian groups by Peters. This approach allows us to work with endomorphisms instead of working with automorphisms. We study some of the basic properties of this new entropy and we give direct proofs of the formulae that allow one to compute the entropy of endomorphisms of Z{double-struck} N, R{double-struck} N and C{double-struck} N, for every positive integer N. © 2012 Elsevier B.V.
Original language | English |
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Pages (from-to) | 2546-2556 |
Journal | Topology and its Applications |
Volume | 159 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1 Jun 2012 |
Keywords
- Algebraic entropy
- Continuous endomorphisms
- Haar measure
- Locally compact abelian groups