The topological entropy of powers on Lie groups

Abstract In this paper, we address the problem of computing topological entropy a map $\psi : G \to G$ , where is Lie group, given by some power (g) = g^k$ with k positive integer. When abelian, $ an endomorphism and its $h(\psi ) \dim (T(G)) \log (k)$ $T(G)$ maximal torus as shown Patrão [The endomorphisms groups. Israel J. Math. 234 (2019), 55–80]. However, when not no longer these previous results cannot be used. Still, has interesting symmetries, for example, it commutes conjugations . structure theory groups used to show that (T)\log T generalizing formula in abelian case. particular, powers on compact discrete center always positive, contrast what happens such groups, which have null entropy.