Anna Giordano Bruno (University of Udine)

May 5, 2020 @ 6:00 am – 8:00 am
Lecture held in Elysium

Title: Topological Entropy and Algebraic Entropy on Locally Compact Abelian Groups
by Anna Giordano Bruno (University of Udine) as part of Topological Groups

Lecture held in Elysium.

Since its origin, the algebraic entropy $h_{alg}$ was introduced in connection with the topological entropy $h_{top}$ by means of Pontryagin duality. For a continuous endomorphism $phicolon Gto G$ of a locally compact abelian group $G$, denoting by $widehat G$ the Pontryagin dual of $G$ and by $widehat phicolon Gto G$ the dual endomorphism of $phi$, we prove that $$h_{top}(phi)=h_{alg}(widehatphi)$$ under the assumption that $G$ is compact or that $G$ is totally disconnected. It is known that this equality holds also when $phi$ is a topological automorphism.