International Journal of Mathematics and Mathematical Sciences

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International Journal of Mathematics and Mathematical Sciences / 2000 / Article

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Volume 24 |Article ID 489573 | 7 pages | https://doi.org/10.1155/S0161171200004282

About the existence of the thermodynamic limit for some deterministic sequences of the unit circle

Stefano Siboni1

1Dipartimento di Ingegneria dei Materiali, Facoltà di Ingegneria, Università di Trento, Mesiano, Italy

Received20 Dec 1999

Abstract

We show that in the set Ω=ℝ+×(1,+∞)⊂ℝ+2, endowed with the usual Lebesgue measure, for almost all (h,λ)∈Ω the limit limn→+∞(1/n)ln|h(λn−λ−n)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.

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.

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