A4 Vertaisarvioitu artikkeli konferenssijulkaisussa
Everywhere Zero Pointwise Lyapunov Exponents for Sensitive Cellular Automata
Tekijät: Hotanen Toni
Toimittaja: Hector Zenil
Konferenssin vakiintunut nimi: International Workshop on Cellular Automata and Discrete Complex Systems
Kustantaja: Springer Science and Business Media Deutschland GmbH
Julkaisuvuosi: 2020
Lehti: Lecture Notes in Computer Science
Kokoomateoksen nimi: Cellular Automata and Discrete Complex Systems 26th IFIP WG 1.5 International Workshop, AUTOMATA 2020, Stockholm, Sweden, August 10–12, 2020, Proceedings
Tietokannassa oleva lehden nimi: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Sarjan nimi: Lecture Notes in Computer Science
Vuosikerta: 12286
Aloitussivu: 71
Lopetussivu: 85
ISBN: 978-3-030-61587-1
eISBN: 978-3-030-61588-8
ISSN: 0302-9743
DOI: https://doi.org/10.1007/978-3-030-61588-8_6
Lyapunov exponents are an important concept in differentiable dynamical systems and they measure stability or sensitivity in the system. Their analogues for cellular automata were proposed by Shereshevsky and since then they have been further developed and studied. In this paper we focus on a conjecture claiming that there does not exist such a sensitive cellular automaton, that would have both the right and the left pointwise Lyapunov exponents taking the value zero, for each configuration. In this paper we prove this conjecture false by constructing such a cellular automaton, using aperiodic, complete Turing machines as a building block.
