## Abstract

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 give

all 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 aforementioned

regions nor to the nite region 1 r0 4=3;r0 r1 < r0 1, then r only has

the trivial bounded orbit 0, which is a natural generalization of the established niteness property

for SRS with non-periodic orbits. The further reduction should be quite involving, because for all

1 r0 < 4=3 there exists at least one interval I such that for the point (r0; r1) this is not true

whenever r1 2 I.

The aim of the present paper is to describe such unusual points as well as possible. We give

all 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 aforementioned

regions nor to the nite region 1 r0 4=3;r0 r1 < r0 1, then r only has

the trivial bounded orbit 0, which is a natural generalization of the established niteness property

for SRS with non-periodic orbits. The further reduction should be quite involving, because for all

1 r0 < 4=3 there exists at least one interval I such that for the point (r0; r1) this is not true

whenever r1 2 I.

Original language | English |
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Article number | A50 |

Number of pages | 20 |

Journal | INTEGERS: Electronic Journal of Combinatorial Number Theory |

Volume | 19.2019 |

Publication status | Published - 2019 |