Displaying similar documents to “Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems”

Dynamical directions in numeration

Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner (2006)

Annales de l’institut Fourier

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This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to β -numeration and its generalisations, abstract numeration...

Periodic Jacobi-Perron expansions associated with a unit

Brigitte Adam, Georges Rhin (2011)

Journal de Théorie des Nombres de Bordeaux

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We prove that, for any unit ϵ in a real number field K of degree n + 1 , there exits only a finite number of n-tuples in  K n which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for n = 1 . For n = 2 we give an explicit algorithm to compute all these pairs.

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β -shifts

Veronica Baker, Marcy Barge, Jaroslaw Kwapisz (2006)

Annales de l’institut Fourier

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This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.

Existence of periodic solutions for semilinear parabolic equations

Norimichi Hirano, Noriko Mizoguchi (1996)

Banach Center Publications

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In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if ( t , x ) ∈ R + × Ω u = 0 if ( t , x ) ∈ R + × ∂ Ω , where Ω ⊂ R N is a bounded domain with smooth boundary ∂Ω and g : R + × Ω ¯ × R → R is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.

Basic properties of shift radix systems.

Akiyama, Shigeki, Borbély, Tibor, Brunotte, Horst, Pethő, Attila, Thuswaldner, Jörg M. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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