On the partitions with Sturmian-like refinements
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00443912" target="_blank" >RIV/67985556:_____/15:00443912 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/15:00209255
Result on the web
<a href="http://dx.doi.org/10.3934/dcds.2015.35.3483" target="_blank" >http://dx.doi.org/10.3934/dcds.2015.35.3483</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2015.35.3483" target="_blank" >10.3934/dcds.2015.35.3483</a>
Alternative languages
Result language
angličtina
Original language name
On the partitions with Sturmian-like refinements
Original language description
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 aone-sided Sturmian subshift, satisfying a mild technical assumption, the sliding block code of sufficiently large length induced by the mapping is injective.
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/GP13-35273P" target="_blank" >GP13-35273P: Algorithms for circular morphisms and their fixed points</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems
ISSN
1078-0947
e-ISSN
—
Volume of the periodical
35
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
3483-3501
UT code for WoS article
000353473300011
EID of the result in the Scopus database
2-s2.0-84923773018