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Scale function vs Topological entropy

2012/10/05 by Federico Berlai, Berlai, Federico, Dikran Dikranjan +3
Mathematics · #22D05 #22D40 #37B40 #54C70 #54H11 #54H20 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #math.GN #math.GR #msc:22D05 #msc:22D40 #msc:37B40 #msc:54C70 #msc:54H11 #msc:54H20

paper · pdf · doi:10.48550/arxiv.1210.1749

21 pages

arxiv created 2013/06/06 · arxiv updated 2013/06/07

Abstract

In the realm of topological automorphisms of totally disconnected locally compact groups, the scale function introduced by Willis in \citeWillis is compared with the topological entropy. We prove that the logarithm of the scale function is always dominated by the topological entropy and we provide examples showing that this inequality can be strict. Moreover, we give a condition equivalent to the equality between these two invariants. Various properties of the scale function, inspired by those of the topological entropy, are presented.

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