著者

Akiyama Shigeki Zaimi Toufik

出版者

SP Versita

雑誌

Central European Journal of mathematics (ISSN:18951074)

巻号頁・発行日

vol.11, no.9, pp.1616-1627, 2013-09

被引用文献数

2 2

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A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus greater than one. Expecting the converse of the last statement is true, we show some theoretical and experimental results, which support this conjecture.

著者

Abe Toshikazu Akiyama Shigeki Hatori Osamu

出版者

Elsevier

雑誌

Linear algebra and its applications (ISSN:00243795)

巻号頁・発行日

vol.439, no.1, pp.174-188, 2013-07

被引用文献数

9

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In this paper we describe all isometries on the special orthogonal group. As an application we give a form of spectrally multiplicative map on the special orthogonal group.

著者

AKIYAMA SHIGEKI PETH˝O ATTILA

出版者

IOP Publishing Ltd & London Mathematical Society

雑誌

Nonlinearity (ISSN:09517715)

巻号頁・発行日

vol.26, pp.871-880, 2013-03

被引用文献数

5 5

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For a fixed λ ∈ (−2, 2), we study a family of discretizedrotation on Z2 defined by(x, y) 7→ (y, −⌊x + λy⌋).We prove that this reversible dynamics has infinitely many periodic orbits.

著者

Akiyama Shigeki Komornik Vilmos

出版者

Elsevier

雑誌

Journal of number theory (ISSN:0022314X)

巻号頁・発行日

vol.133, no.2, pp.375-390, 2013-02

被引用文献数

16

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By the m-spectrum of a real number q>1 we mean the set Ym(q) of values p(q) where p runs over the height m polynomials with integer coefficients. These sets have been extensively investigated during the last fifty years because of their intimate connections with infinite Bernoulli convolutions, spectral properties of substitutive point sets and expansions in noninteger bases. We prove that Ym(q) has an accumulation point if and only if q<m+1 and q is not a Pisot number. Consequently a number of related results on the distribution of points of this form are improved.