International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 12, Pages 857-863
doi:10.1155/S0161171200004282
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle
Stefano Siboni
Dipartimento di Ingegneria dei Materiali, Facoltà di Ingegneria, Università di Trento, Mesiano, Trento 38050, Italy
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.