International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 12, Pages 857-863
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle
Dipartimento di Ingegneria dei Materiali, Facoltà di Ingegneria, Università di Trento, Mesiano, Trento 38050, Italy
Received 20 December 1999
Copyright © 2000 Stefano Siboni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We show that in the set , endowed with the usual Lebesgue
measure, for almost all the limit
exists and is equal to zero. The result is related to a characterization of relaxation to equilibrium in mixing
automorphisms of the two-torus. It is nothing but a curiosity, but maybe you will find it nice.