Global metric regularity of the devil’s staircase of topological entropy
Ke‐Fei Cao, Zhong-Xuan Chen, Shou-Li Peng · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1995
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.