About the existence of the thermodynamic limit for some deterministic sequences of the unit circle. (15th December 2000) - Siboni, Stefano
Abstract : We show that in the setΩ = ℝ + × ( 1, + ∞ ) ⊂ ℝ + 2, endowed with the usual Lebesgue measure, for almost all( h, λ ) ∈ Ω the limitlim 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.