Preprints, Working Papers, ... Year : 2017

The generic limit set of cellular automata

Abstract

In this article, we consider a topological dynamical system. The generic limit set is the smallest closed subset which has a comeager realm of attraction. We study some of its topological properties, and the links with equicontinuity and sensitivity. We emphasize the case of cellular automata, for which the generic limit set is included in all subshift attractors, and discuss directional dynamics, as well as the link with measure-theoretical similar notions.

Domains

Dynamical Systems [math.DS]
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Pierre Guillon  : Connect in order to contact the contributor

https://hal.science/hal-01861590

Submitted on : Wednesday, November 8, 2023-10:42:13 AM

Last modification on : Friday, December 27, 2024-12:06:02 PM

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Dates and versions

hal-01861590 , version 1 (24-08-2018)
hal-01861590 , version 2 (24-04-2019)
hal-01861590 , version 3 (08-11-2023)

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Saliha Djenaoui, Pierre Guillon. The generic limit set of cellular automata. 2017. ⟨hal-01861590v3⟩

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CNRS UNIV-AMU EC-MARSEILLE INSMI I2M I2M-2014- TDS-MACS
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