Expansions in multiple bases over general alphabets

Komornik, Vilmos; Lü, Jian; Zou, Yuru

doi:10.1007/s10474-022-01231-4

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Cantor Real Bases and Alternate Bases1

Introduction1

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2023

2024

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Cited by 5 publications

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“…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%

Alternate Base Numeration Systems

Charlier

2023

Lecture Notes in Computer Science

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Alternate base numeration systems generalize real base numeration systems as defined by Renyi. Real numbers are represented using a finite number of bases periodically. Such systems naturally appear when considering linear numeration systems without a dominant root. As it happens, many classical results generalize to these numeration systems with multiple bases but some don't. This is a survey of the work done so far concerning combinatorial, algebraic and dynamical aspects. This study has been led in collaboration with several co-authors :

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“…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%

Alternate Base Numeration Systems

Charlier

2023

Lecture Notes in Computer Science

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show abstract

“…Beside b-adic expansions and continued fraction expansions many other expansions of real number are studied. We have ergodic and dimension theoretical results on β-expansions [29,2], Cantor series expansions [9,16,1], Engel-expansions [10,31,12], Lüroth-expansions [20,4], multiple-base expansions [25,25,22,18] and others. In this paper we introduce a new family of expansions of real numbers which is given essentially by the expression in the abstract.…”

Section: Introductionmentioning

confidence: 99%