MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

作者：Fang, Lulu; Ma, Jihua; Song, Kunkun^*; Wu, Min

来源：Acta Mathematica Scientia, 2021, 41(6): 1896-1910.

DOI：10.1007/s10473-021-0607-1

• multifractal analysis
• convergence exponent
• continued fractions

Let x is an element of (0, 1) be a real number with continued fraction expansion [a(1) (x), a(2)(x), a(3) (x), ...]. This paper is concerned with the multifractal spectrum of the convergence exponent of {a(n)(x)}(n >= 1) defined by @@@ tau(x) := inf {s >= 0 : Sigma(n >= 1) a(n)(-s) (x) < infinity}.

• 单位
  武汉大学; 南京理工大学