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

Stefano Siboni

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-7

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 lim n → + ∞ ( 1 / n ) ln | h ( λ n − λ − n ) mod [ - 1 2 , 1 2 ) | 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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:489573

DOI: 10.1155/S0161171200004282

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