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001-es BibID:BIBFORM008051
Első szerző:Akiyama, Shigeki (matematikus)
Cím:Generalized radix representations and dynamical systems III. / Akiyama, S., Brunotte, H., Pethő, A., Thuswaldner, J. M.
Dátum:2008
ISSN:0030-6126
Megjegyzések:For r = (r(1),...,r(d)) is an element of R-d the map tau(r) : Z(d) -> Z(d) given by tau r(a(1),...,a(d)) = (a(2),...,a(d), -[r(1)a(1)+...+r(d)a(d)]) is called a shift radix system if for each a is an element of Z(d) there exists an integer k > 0 with tau(k)(r)(a) = 0. As shown in the first two parts of this series of papers shift radix systems lire intimately related to certain well-known notions of number systems like beta-expansions and canonical number systems. In the present paper further structural relationships between shift radix systems and canonical number systems are investigated. Among other results we show that canonical number systems related to polynomials Sigma(d)(i=0) p(i)X(i) is an element of Z[X] of degree d with a large but fixed constant term p(0) approximate the set of (d - 1)-dimensional shift radix systems. The proofs make extensive use of the following tools: Firstly, vectors r is an element of R-d which define shift radix systems lire strongly connected to monic real polynomials all of whose roots lie inside the unit circle. Secondly, geometric considerations which were established in Part I of this series of papers are exploited. The main results establish two conjectures mentioned in Part II of this series of papers.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
Megjelenés:Osaka Journal of Mathematics. - 45 : 2 (2008), p. 347-374. -
További szerzők:Brunotte, Horst Pethő Attila (1950-) (matematikus, informatikus) Thuswaldner, Jörg M. (matematikus)
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