Global metric regularity of the devil's staircase of topological entropy.

Abstract

In this paper, the global metric regularity of the devil's staircase of topological entropy is discussed by employing the quadratic map f(x)=1-\ensuremath{\lambda}${\mathit{x}}^{2}$ as an actual metric model. The generalized dimensions, singularity spectra, ``free energy,'' and the similarity between subintervals with an infinite number of scales in the entropy staircase are calculated. A lower bound 0.86 of chaotic measure in the entropy staircase is obtained.