Lyapunov Exponents Vs Expansivity and Sensitivity in Cellular Automata

Finelli, Michele; Manzini, Giovanni; Margara, Luciano

doi:10.1007/978-1-4471-0941-9_6

Cited by 2 publications

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“…Connections between various dynamical properties of cellular automata and possible values of Lyapunov exponents have been studied for example in [5], [4] and [2]. In [4], a closed formula for calculating the value of the shift-invariant Lyapunov exponents, was presented in the setting of linear cellular automata.…”

Section: Introductionmentioning

confidence: 99%

“…In [4], a closed formula for calculating the value of the shift-invariant Lyapunov exponents, was presented in the setting of linear cellular automata. In [5], the authors proved that for a given positively expansive cellular automaton, the shift-invariant Lyapunov exponents are positive for each configuration. The result was later improved in [2], where it was shown that the same result holds for the pointwise Lyapunov exponents.…”

Section: Introductionmentioning

confidence: 99%

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Everywhere Zero Pointwise Lyapunov Exponents for Sensitive Cellular Automata

Hotanen

2020

Lecture Notes in Computer Science

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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.

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