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Entropy for endomorphisms of LCA groups. (English) Zbl 1243.22007
The author introduces a modified version of the entropy defined for locally compact abelian groups by J. Peters [Pac. J. Math. 96, 475–488 (1981; Zbl 0478.28010)]. The advantage of this approach is that it allows one to work with endomorphisms instead of automorphisms. After studying some of the basic properties of this new entropy the author gives and proves some formulae to compute the entropy of endomorphisms of \(\mathbb{Z}^N\), \(\mathbb{R}^N\) and \(\mathbb{C}^N\), for every positive integer \(N\).

22D40 Ergodic theory on groups
54H20 Topological dynamics (MSC2010)
28D20 Entropy and other invariants
54C70 Entropy in general topology
Full Text: DOI
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