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THE ORBIT OF A β-TRANSFORMATION CANNOT LIE IN A SMALL INTERVAL
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 Title & Authors
THE ORBIT OF A β-TRANSFORMATION CANNOT LIE IN A SMALL INTERVAL
Kwon, Do-Yong;
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 Abstract
For > 1, let : [0, 1] [0, 1) be the -transformation. We consider an invariant -orbit closure contained in a closed interval with diameter 1/, then define a function by the supremum such -orbit with frequency in base , i.e., the maximum value in -orbit closure. This paper effectively determines the maximal domain of , and explicitly specifies all possible minimal intervals containing -orbits.
 Keywords
-expansion;-transformation;Sturmian word;Christoffel word;
 Language
English
 Cited by
1.
Moments of discrete measures with dense jumps induced by β -expansions, Journal of Mathematical Analysis and Applications, 2013, 399, 1, 1  crossref(new windwow)
2.
A two-dimensional singular function via Sturmian words in base β, Journal of Number Theory, 2013, 133, 11, 3982  crossref(new windwow)
3.
A one-parameter family of Dirichlet series whose coefficients are Sturmian words, Journal of Number Theory, 2015, 147, 824  crossref(new windwow)
4.
Exceptional parameters of linear mod one transformations and fractional parts {ξ(p/q)n}, Comptes Rendus Mathematique, 2015, 353, 4, 291  crossref(new windwow)
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