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International Journal of Mathematics and Mathematical Sciences
Volume 24, 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 Hindawi Publishing Corporation. 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 Ω=+×(1,+)+2, endowed with the usual Lebesgue measure, for almost all (h,λ)Ω the limit limn+(1/n)ln|h(λnλn)mod[-12,12)| 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.