2013/10/24 by Dikran Dikranjan, Dikranjan, Dikran, Anna Giordano Bruno +1
Mathematics · #20K30 #22B05 #22D40 #37B40 #54H11 #54H20 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #math.GN #math.GR #msc:20K30 #msc:22B05 #msc:22D40 #msc:37B40 #msc:54H11 #msc:54H20
paper · pdf · doi:10.48550/arxiv.1310.6665
arxiv created 2013/10/24 · arxiv updated 2013/10/25
For a totally disconnected locally compact abelian group, we prove that the topological entropy of a continuous endomorphism coincides with the algebraic entropy of the dual endomorphism with respect to the Pontryagin duality. Moreover, this result is extended to all locally compact abelian groups under the assumption of additivity with respect to some fully invariant subgroups for both the topological and the algebraic entropy.