The multifractal spectra of certain planar recurrence sets in the continued fraction dynamical system

作者：Chen Haibo^*; Wen Zhixiong; Yu Min

来源：Journal of Mathematical Analysis and Applications, 2015, 422(2): 1264-1276.

DOI：10.1016/j.jmaa.2014.09.023

• Hausdorff dimension
• Continued fraction
• Quantitative hitting time indicator
• Cut set

In this paper, we will introduce and study the planar recurrence level set
S(alpha, beta) := {(x, y) is an element of [0, 1)(2): (R) under bar(x, y) = alpha, (R) over bar (x, y) = beta}, 0 <= alpha <= beta <= infinity,
where (R) under bar(x, y) and (R) over bar (x, y) are the lower and upper quantitative hitting time indicators of y by x respectively in the continued fraction dynamical system. It is shown that the multifractal spectrum is always degenerate in a sense that it is constant independent of the choice of the level set.

• 单位
  中南大学