0443912 20240103210044.720150528235959.9 000353473300011 84923773018 10.3934/dcds.2015.35.3483 19 s. P cav_un_epca*02558981078-0947358 (2015)3483-3501AIMS Press Coding of rotation Sturmian subshift Toeplitz subshift factor mapping low-complexity system sliding block-code Sturmian partition local rule cav_un_auth*0219359 Kupsa Michal Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics 85 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0316720 Starosta Š. CZ 15 In the dynamics of a rotation of the unit circle by an irrational angle $/alpha/in(0,1)$, we study the evolution of partitions whose atoms are finite unions of left-closed right-open intervals with endpoints lying on the past trajectory of the point $0$. Unlike the standard framework, we focus on partitions whose atoms are disconnected sets. We show that the refinements of these partitions eventually coincide with the refinements of a preimage of the Sturmian partition, which consists of two intervals $[0,1-/alpha)$ and $[1-/alpha,1)$. In particular, the refinements of the partitions eventually consist of connected sets, i.e., intervals. We reformulate this result in terms of Sturmian subshifts: we show that for every non-trivial factor mapping from a one-sided Sturmian subshift, satisfying a mild technical assumption, the sliding block code of sufficiently large length induced by the mapping is injective. 2016 BA 4 A hod 4ah 20231122140942.3 RVO:67985556 http://hdl.handle.net/11104/0246860 cav_un_auth*0300911 ČVUT České vysoké učení technické v Praze, Fakulta informačních technologií CZ 1 Department of Stochastic Informatics UTIA-B 10101 MATHEMATICS S MATHEMATICS|MATHEMATICS.APPLIED 1.168 0.353 5.8 0.01809 1.03 2790 1.568 Q1 1.047 272 Q1 80.279 79.1 Q1 Q1* 86.699 2015 Soubory v repozitáři: kupsa-0443912.pdf 84923773018 SCOPUS 000353473300011 WOS cav_un_epca*0255898 Discrete and Continuous Dynamical Systems 1078-0947 1553-5231 Roč. 35 č. 8 2015 3483 3501 AIMS Press