About the existence of the thermodynamic limit for some deterministic sequences of the unit circle. (15th December 2000)

• Record Type: Journal Article
• Authors: Siboni, Stefano
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 24:Number 12(2000)
• Page Start: 857
• Page End: 863
• Publication Date: 2000-12-15
• Subjects: Thermodynamic limit -- Borel-Cantelli argument; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171200004282
• Languages: English
• ISSNs: 0161-1712

Abstract

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.