Ústav teorie informace a automatizace

Jste zde

Bibliografie

Journal Article

On the partitions with Sturmian-like refinements

Kupsa Michal, Starosta Š.

: Discrete and Continuous Dynamical Systems vol.35, 8 (2015), p. 3483-3501

: Coding of rotation, Sturmian subshift, Toeplitz subshift, factor mapping, low-complexity system, sliding block-code, Sturmian partition, local rule

: 10.3934/dcds.2015.35.3483

(eng): 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.

: BA

07.01.2019 - 08:39