Adjoint entropy vs topological entropy

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• 作者：Anna Giordano Bruno¹ ; ^{anna.giordanobruno@uniud.it}
• 关键词：primary ; 20K30 ; secondary ; 28D20 ; 22D35
• 刊名：Topology and its Applications
• 出版年：2012
• 出版时间：1 June, 2012
• 年：2012
• 卷：159
• 期：9
• 页码：2404-2419
• 全文大小：258 K

文摘

Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied in Dikranjan (2010) . We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the topological adjoint entropy with the known topological entropy of continuous endomorphisms of compact abelian groups. In particular, the topological adjoint entropy and the topological entropy coincide on continuous endomorphisms of totally disconnected compact abelian groups. Moreover, we prove two so-called Bridge Theorems between the topological adjoint entropy and the algebraic entropy using respectively the Pontryagin duality and the precompact duality.