Everywhere Zero Pointwise Lyapunov Exponents for Sensitive Cellular Automata

: Hotanen Toni

: Hector Zenil

: International Workshop on Cellular Automata and Discrete Complex Systems

Publisher: Springer Science and Business Media Deutschland GmbH

: 2020

: Lecture Notes in Computer Science

: Cellular Automata and Discrete Complex Systems 26th IFIP WG 1.5 International Workshop, AUTOMATA 2020, Stockholm, Sweden, August 10–12, 2020, Proceedings

: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

: Lecture Notes in Computer Science

: 12286

: 71

: 85

: 978-3-030-61587-1

: 978-3-030-61588-8

: 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.