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.

The Bridge Theorem for totally disconnected LCA groups

DIKRANJAN, Dikran;GIORDANO BRUNO, Anna
2014-01-01

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/892155
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