2020
DOI: 10.1007/s10474-020-01094-7
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Expansions in multiple bases

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Cited by 10 publications
(6 citation statements)
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“…In section 2.2. we see that multiple base expansions of x ∈ [0, 1], whose properties have been investigated recently (e.g. [20] and [23]), are generated by such a random dynamical system. In particular, we give a sufficient condition to guarantee 'almost all' expansions actually converge to x ∈ [0, 1].…”
Section: Preliminariesmentioning
confidence: 97%
“…In section 2.2. we see that multiple base expansions of x ∈ [0, 1], whose properties have been investigated recently (e.g. [20] and [23]), are generated by such a random dynamical system. In particular, we give a sufficient condition to guarantee 'almost all' expansions actually converge to x ∈ [0, 1].…”
Section: Preliminariesmentioning
confidence: 97%
“…The same framework was introduced simultaneously in [6]. Moreover, other kinds of expansions with multiple real bases were also recently studied, see [23,25,28].…”
Section: Cantor Real Bases and Alternate Basesmentioning
confidence: 99%
“…Representations of real numbers involving more than one base simultaneously and independently aroused the interest of other mathematicians [4,14,16,23]. But so far, most of the research was concentrated on the combinatorial properties of these representations as in [6] and not on their dynamical or algebraic properties which are studied respectively in [7] and in this paper.…”
Section: Introductionmentioning
confidence: 96%