A note on the lévy constant for continued fractions

In this note, we study the lévy constant of continued fraction expansions. We show that for all x \in [0,1), the upper lévy constant of x is finite except a set with Hausdorff dimension one-half.

Anahtar Kelimeler:

Continued fractions, lévy constant, Hausdorff dimension.

A note on the lévy constant for continued fractions

In this note, we study the lévy constant of continued fraction expansions. We show that for all x \in [0,1), the upper lévy constant of x is finite except a set with Hausdorff dimension one-half.

Keywords:

Continued fractions, lévy constant, Hausdorff dimension.,

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Department of Mathematics, Jishou University Zhangjiajie, Hunan, 427000, P.R. CHINA e-mail: zhongting 2005@126.com