Corpus ID: 235458385

Local non-periodic order and diam-mean equicontinuity on cellular automata

@inproceedings{Banos2021LocalNO,
  title={Local non-periodic order and diam-mean equicontinuity on cellular automata},
  author={Luguis de los Santos Banos and Felipe Garc'ia-Ramos},
  year={2021}
}
Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of “local” skew product between a shift and an odometer looking cellular automaton (CA) we will show there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous, and hence not almost locally periodic. 
1 Citations
Diameter mean equicontinuity and cellular automata
Mean and diam-mean equicontinuity are dynamical properties that have been of use in the study of non-periodic order. We show that the Pacman automaton is not almost diam-mean equicontinuous (it isExpand

References

SHOWING 1-10 OF 27 REFERENCES
Bounded complexity, mean equicontinuity and discrete spectrum
We study dynamical systems that have bounded complexity with respect to three kinds metrics: the Bowen metric $d_{n}$ , the max-mean metric $\hat{d}_{n}$ and the mean metric $\bar{d}_{n}$ , both inExpand
Diameter mean equicontinuity and cellular automata
Mean and diam-mean equicontinuity are dynamical properties that have been of use in the study of non-periodic order. We show that the Pacman automaton is not almost diam-mean equicontinuous (it isExpand
Garćıa-Ramos. Diameter mean equicontinuity and cellular automata
  • Conference proceedings of AUTOMATA
  • 2021
Mean equicontinuity, complexity and applications
We will review the recent development of the research related to mean equicontinuity, focusing on its characterizations, its relationship with discrete spectrum, topo-isomorphy, and boundedExpand
Mean equicontinuity, complexity and applications. Discrete and Continuous Dynamical Systems
  • 2021
Mean equicontinuity and mean sensitivity on cellular automata
We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full-shiftExpand
Mean equicontinuity, almost automorphy and regularity
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when anExpand
The structure of mean equicontinuous group actions
We study mean equicontinuous actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. In this setting, we establish the equivalence of mean equicontinuity andExpand
Limit behaviour of μ-equicontinuous cellular automata
TLDR
It is shown that under some conditions the sequence of Cesaro averages of a measure µ, converge under the actions of a µ-equicontinuity CA, which is a uniform Bernoulli measure with respect to the CA. Expand
What is Aperiodic Order
The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order,Expand
...
1
2
3
...