Dimension of some non-normal continued fraction sets
2008 ◽
Vol 145
(1)
◽
pp. 215-225
◽
AbstractWe consider certain sets of non-normal continued fractions for which the asymptotic frequencies of digit strings oscillate in one or other ways. The Hausdorff dimensions of these sets are shown to be the same value 1/2 as long as they are non-empty. An interesting example among them is the set of “extremely non-normal continued fractions” which was previously conjectured to be of Hausdorff dimension 0.
Keyword(s):
2020 ◽
Vol 16
(07)
◽
pp. 1433-1447
Keyword(s):
2014 ◽
Vol 10
(04)
◽
pp. 849-857
◽
2009 ◽
Vol 148
(1)
◽
pp. 179-192
◽
2017 ◽
Vol 13
(09)
◽
pp. 2433-2443
Keyword(s):
Keyword(s):
2009 ◽
Vol 29
(1)
◽
pp. 73-109
◽
2020 ◽
Vol 102
(2)
◽
pp. 196-206