Nonextensive Statistical Mechanics

198 5 Deterministic Dynamical Foundations of Nonextensive Statistical MechanicsFig. 5.48 Log–log plots of ˜λ maxNvs. N for typical values of α and u = 5. The full lines are thebest fittings with the heuristic forms (a − b/N)/(N ⋆ ) c . Consequently, ˜λ maxN∼ 1/N κ(α) ,whereκ ispositive for 0 ≤ α1. For α = 1, ˜λ maxNis expected to vanish like somepower of 1/ ln N (from [177]).Fig. 5.49 Log–log plots of ˜λ maxNvs. N for typical values of α and u = 5: d = 2(top panel) andd = 3(bottom panel). The full lines are the best fittings with the heuristic forms (a − b/N)/(N ⋆ ) c .Consequently, ˜λ maxN∼ 1/N κ(α,d) ,whereκ is positive for 0 ≤ α/d < 1 and vanishes for α/d > 1.For α/d = 1, ˜λ maxNis expected to vanish like some power of 1/ ln N (from [178]).