Non-trivial matrix actions preserve normality for continued fractions
2017 ◽
Vol 153
(2)
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pp. 274-293
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Keyword(s):
A seminal result due to Wall states that if $x$ is normal to a given base $b$, then so is $rx+s$ for any rational numbers $r,s$ with $r\neq 0$. We show that a stronger result is true for normality with respect to the continued fraction expansion. In particular, suppose $a,b,c,d\in \mathbb{Z}$ with $ad-bc\neq 0$. Then if $x$ is continued fraction normal, so is $(ax+b)/(cx+d)$.
1985 ◽
Vol 39
(3)
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pp. 300-305
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2009 ◽
Vol 29
(5)
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pp. 1451-1478
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2018 ◽
Vol 2019
(19)
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pp. 6136-6161
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1991 ◽
Vol 51
(2)
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pp. 324-330
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1987 ◽
Vol 30
(2)
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pp. 295-299
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2001 ◽
Vol 64
(2)
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pp. 331-343
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