This article is cited in 9 papers

The Entropy of an Automorphism of a Solenoidal Group

L. M. Abramov

Kolomna

Abstract: Let us denote by $X$ a group of characters for the subgroup $R$ of an additive group of rational numbers and by $T$ its automorphism adjoint to the automorphism of the group $R$, which is given by multiplying by the irreducible fraction ${m/n}$. In this paper it is proved that the entropy of such an automorphism equals $\log(\max\{|m|,n\})$.

Received: 09.03.1959

 English version: Theory of Probability and its Applications, 1959, 4:3, 231–236