TY - JOUR

T1 - The finiteness property for shift radix systems with general parameters

AU - Pethõ, Attila

AU - Thuswaldner, Jörg

AU - Weitzer, Mario Franz

PY - 2019

Y1 - 2019

N2 - There are two-dimensional expanding shift radix systems (SRS) which have some periodic orbits.The aim of the present paper is to describe such unusual points as well as possible. We giveall regions that contain parameters the corresponding SRS of which generate obvious cycles like(1); (1); (1;1); (1; 0); (1; 0). We prove that if r = (r0; r1) 2 R2 neither belongs to the aforementionedregions nor to the nite region 1 r0 4=3;r0 r1 < r0 1, then r only hasthe trivial bounded orbit 0, which is a natural generalization of the established niteness propertyfor SRS with non-periodic orbits. The further reduction should be quite involving, because for all1 r0 < 4=3 there exists at least one interval I such that for the point (r0; r1) this is not truewhenever r1 2 I.

AB - There are two-dimensional expanding shift radix systems (SRS) which have some periodic orbits.The aim of the present paper is to describe such unusual points as well as possible. We giveall regions that contain parameters the corresponding SRS of which generate obvious cycles like(1); (1); (1;1); (1; 0); (1; 0). We prove that if r = (r0; r1) 2 R2 neither belongs to the aforementionedregions nor to the nite region 1 r0 4=3;r0 r1 < r0 1, then r only hasthe trivial bounded orbit 0, which is a natural generalization of the established niteness propertyfor SRS with non-periodic orbits. The further reduction should be quite involving, because for all1 r0 < 4=3 there exists at least one interval I such that for the point (r0; r1) this is not truewhenever r1 2 I.

M3 - Article

VL - 19.2019

JO - INTEGERS: Electronic Journal of Combinatorial Number Theory

JF - INTEGERS: Electronic Journal of Combinatorial Number Theory

SN - 1867-0652

M1 - A50

ER -