The Entropy of an Automorphism of a Solenoidal Group
Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 3, pp. 249-254
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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 $\log(\max\{|m|,n\})$.
@article{TVP_1959_4_3_a0,
author = {L. M. Abramov},
title = {The {Entropy} of an {Automorphism} of a {Solenoidal} {Group}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {249--254},
year = {1959},
volume = {4},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1959_4_3_a0/}
}
L. M. Abramov. The Entropy of an Automorphism of a Solenoidal Group. Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 3, pp. 249-254. http://geodesic.mathdoc.fr/item/TVP_1959_4_3_a0/