Results 1 to 10 of about 15,510 (221)
Journal of the London Mathematical Society, 2023 AbstractWe describe the infinite interval exchange transformations, called the rotated odometers, which are obtained as compositions of finite interval exchange transformations and the von Neumann–Kakutani map. We show that with respect to Lebesgue measure on the unit interval, every such transformation is measurably isomorphic to the first return map ...
Henk Bruin, Olga Lukina
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Odometers on Regular Languages [PDF]
Theory of Computing Systems, 2005 Odometers or "adding machines" are usually introduced in the context of positional numeration systems built on a strictly increasing sequence of integers. We generalize this notion to systems defined on an arbitrary infinite regular language. In this latter situation, if (A,
Valérie Berthé, Michel Rigo
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$Z^{d}$-odometers and cohomology [PDF]
, 2017 Cohomology for actions of free abelian groups on the Cantor set has (when endowed with an order structure) provided a complete invariance for orbit equivalence. In this paper, we study a particular class of actions of such groups called odometers (or profinite actions) and investigate their cohomology. We show that for a free, minimal $\Z^{d}$-odometer,
Thierry Giordano +2 more
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Rotated Odometers and Actions on Rooted Trees [PDF]
Fundamenta Mathematicae, 2021 A rotated odometer is an infinite interval exchange transformation (IET) obtained as a composition of the von Neumann-Kakutani map and a finite IET of intervals of equal length. In this paper, we consider rotated odometers for which the finite IET is of intervals of length $2^{-N}$, for some $N \geq 1$.
Henk Bruin, Olga Lukina
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Linear Recursive Odometers and Beta-Expansions [PDF]
Uniform distribution theory, 2016 AbstractThe aim of this paper is to study the connection between different properties related toβ-expansions. In particular, the relation between two conditions, both ensuring purely discrete spectrum of the odometer, is analyzed. The first one is the so-called Hypothesis B for theG-odometers and the second one is denoted by (QM) and it has been ...
Maria Rita Iacò +2 more
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Embedding odometers in cellular automata [PDF]
Fundamenta Mathematicae, 2009 We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be be embedded in a gliders with reflecting walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton, which is a group endomorphism on an n-letter group, and where n ...
Ethan M. Coven, Reem Yassawi
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Linear dynamics induced by odometers [PDF]
Proceedings of the American Mathematical Society, 2022 Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing a variety of dynamical properties. Recently, a systematic study of dynamical properties of composition operators on L p L^p spaces has been initiated.
Donatella Bongiorno +3 more
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Israel Journal of Mathematics, 2022 Construction sequences are a general method of building symbolic shifts that capture cut-and-stack constructions and are general enough to give symbolic representations of Anosov-Katok diffeomorphisms. We show here that any finite entropy system that has an odometer factor can be represented as a special class of construction sequences, the odometer ...
Foreman, Matthew, Weiss, Benjamin
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Science China Mathematics, 2023 We discuss various aspects of noncommutative geometry of smooth subalgebras of Bunce-Deddens-Toeplitz Algebras.
Klimek, Slawomir +2 more
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Subfactors of index less than 5, part 1: the principal graph odometer [PDF]
, 2010 In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$.
A. Ocneanu +22 more
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