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Fractal Tiles Associated with Shift Radix Systems by Valérie Berthé; Anne Siegel; Wolfgang Steiner; Paul Surer; Jörg M. Thuswaldner is a Mathematics article available to read on EtoBox.

What is Fractal Tiles Associated with Shift Radix Systems about?

Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d-dimensional real vector space. They generalize well-known numeration systems such as betaexpansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters r these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (nonmonic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter r of the shift radix system, these tiles provide multiple

Who reads Fractal Tiles Associated with Shift Radix Systems?

Author

Valérie Berthé; Anne Siegel; Wolfgang Steiner; Paul Surer; Jörg M. Thuswaldner

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)

Published

2011

Language

EN

Field

Mathematics (Physical Sciences)