Title of article
A note on the Lyapunov exponent in continued fraction expansions
Author/Authors
Cheng, Jianzhong College of the P.L.A. - Department of the Communication and Commanding, CHINA , Shen, Lu-Ming Agriculture University Changsha - Science college of Hunan, CHINA
From page
145
To page
152
Abstract
Let T : [0, 1) → [0, 1) be the Gauss transformation. For any irrational x ∈ [0, 1), the Lyapunov exponent α(x) of x is defined as alpha(x)=lim_{ntoinfty}frac{1}{n} log |(T^n) (x)|. By Birkoff Average Theorem, one knows that α(x) exists almost surely. However, in this paper, we will see that the non-typical set{xin [0,1):lim_{ntoinfty}frac{1}{n} log |(T^n) (x)| does not exist} carries full Hausdorff dimension
Keywords
Continued fractions , Levy constant , Hausdorff dimension
Journal title
Turkish Journal of Mathematics
Journal title
Turkish Journal of Mathematics
Record number
2530879
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