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.