EXPANSIONS OF REAL NUMBERS IN NON-INTEGER BASES
نویسندگان
چکیده
منابع مشابه
On the Expansions of Real Numbers in Two Integer Bases
Let r ≥ 2 and s ≥ 2 be distinct integers. We establish that, if r and s are multiplicatively independent, then the r-ary expansion and the s-ary expansion of an irrational real number, viewed as infinite words on {0, 1, . . . , r− 1} and {0, 1, . . . , s− 1}, respectively, cannot have simultaneously a low block complexity. In particular, they cannot be both Sturmian words. We also discuss the c...
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Let q > 1 be a real number and let m = m(q) be the largest integer smaller than q. It is well known that each number x ∈ Jq := [0, P ∞ i=1 mq ] can be written as x = P ∞ i=1 ciq −i with integer coefficients 0 ≤ ci < q. If q is a non-integer, then almost every x ∈ Jq has continuum many expansions of this form. In this note we consider some properties of the set Uq consisting of numbers x ∈ Jq ha...
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Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑ ∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which th...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2010
ISSN: 0304-9914
DOI: 10.4134/jkms.2010.47.4.861