SPACE TILINGS AND SUBSTITUTIONS

被引：35

作者：

RADIN, C ^{[1
]}

机构：

[1] UNIV TEXAS,DEPT MATH,AUSTIN,TX 78712

来源：

GEOMETRIAE DEDICATA | 1995年 / 55卷 / 03期

关键词：

Mathematics Subject Classifications (1991): 52C20; 58F11; 47A35;

D O I：

10.1007/BF01266317

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the study of symbolic dynamical systems of finite type and Z(2) action, and the associated use of symbolic substitution dynamical systems, to dynamical systems with R(2) action. The new systems are associated with tilings of the plane. We generalize the classical technique of the matrix of a substitution to include the geometrical information needed to study tilings, and we utilize rotation invariance to eliminate discrete Spectrum. As an example we prove that the pinwheel tilings have no discrete spectrum.

引用

页码：257 / 264

页数：8

共 14 条

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[4]

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[7]

Radin C., Global order from local sources, Bulletin of the American Mathematical Society, 25, pp. 335-364, (1991)

[8]

Radin C., Z<sup>n</sup> versus Z actions for systems of finite type, Contemp. Math., 135, pp. 339-342, (1992)

[9]

Radin C., The pinwheel tilings of the plane, The Annals of Mathematics, 139, 2, pp. 661-702, (1994)

[10]

Radin C., Symmetry of tilings of the plane, Bulletin of the American Mathematical Society, 29, pp. 213-217, (1993)

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