THE PARITIES OF CONTINUED FRACTION

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 4,  2008, pp.733-741
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.4.733
Title & Authors
THE PARITIES OF CONTINUED FRACTION
Ahn, Young-Ho;

Abstract
Let T be Gauss transformation on the unit interval defined by T (x) = $\small{{\frac{1}{x}}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.
Keywords
Gauss transformation;skew product;mod M normal number;Central Limit Theorem;ergodicity;
Language
English
Cited by
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