@inproceedings{a5c652e6ad0344faa606d6233cfcd55c,
title = "Aperiodic points in Z2-subshifts",
abstract = "We consider the structure of aperiodic points in Z2-subshifts, and in particular the positions at which they fail to be periodic. We prove that if a Z2-subshift contains points whose smallest period is arbitrarily large, then it contains an aperiodic point. This lets us characterise the computational di culty of deciding if an Z2-subshift of finite type contains an aperiodic point. Another consequence is that Z2-subshifts with no aperiodic point have a very strong dynamical structure and are almost topologically conjugate to some Z-subshift. Finally, we use this result to characterize sets of possible slopes of periodicity for Z3-subshifts of finite type.",
keywords = "Aperiodicity, Computability, Periodicity, Subshifts of finite type, Tilings, Wang tiles",
author = "Anael Grandjean and \{De Menibus\}, \{Benjamin Hellouin\} and Pascal Vanier",
note = "Publisher Copyright: {\textcopyright} 2018 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.; 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 ; Conference date: 09-07-2018 Through 13-07-2018",
year = "2018",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.ICALP.2018.128",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Christos Kaklamanis and Daniel Marx and Ioannis Chatzigiannakis and Donald Sannella",
booktitle = "45th International Colloquium on Automata, Languages, and Programming, ICALP 2018",
}