Generalized radix representations and dynamical systems. IV

By Shigeki Akiyama, H. Brunotte, A. Pethő, Jörg M. Thuswaldner. 2008

68 citations recorded by the source corpus.

Abstract For r = ( r 1 ,…, r d ) ∈ ℝ d the mapping τ r :ℤ d →ℤ d given by τ r ( a 1 ,…, a d ) = ( a 2 , …, a d ,−⌊ r 1 a 1 +…+ r d a d ⌋) where ⌊·⌋ denotes the floor function, is called a shift radix system if for each a ∈ ℤ d there exists an integer k > 0 with τ r k ( a ) = 0. As shown in Part I of this series of papers, shift radix systems are intimately related to certain well-known notions of number systems like β -expansibns and canonical number systems. After characterization results on shift radix systems in Part II of this series of papers and the thorough investigation of the relations between shift radix systems and canonical number systems in Part III, the present part is devoted to further structural relationships between shift radix systems and β -expansions. In particular we establish the distribution of Pisot polynomials with and without the finiteness property (F).

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e0cb459bb37df57ee876ca579318ad426227a345

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In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On the Pisot Substitution Conjecture (2015, background): “The characterization problem of Pisot numbers with property (F) is difficult and has been transformed into a problem of shift radix systems (see [12, 11]).”
SYMMETRIC SHIFT RADIX SYSTEMS AND FINITE EXPANSIONS (2007, background): “Some partial answers for this problem are given in [5].”