Irrational eigenvalues of D-Dimensional Cellular automata
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915472655515648 |
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| author | Sadi, Nassima Ait Chemlal, Rezki |
| author_facet | Sadi, Nassima Ait Chemlal, Rezki |
| contents | Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both topological and ergodic point of view. The main results of the paper show the impossibility for a cellular automaton with a fully blocking pattern to have a measurable irrational eigenvalues. Further more, a cellular automaton with a set of equicontinuity points of positive measure cannot have a measurable irrational eigenvalue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irrational eigenvalues of D-Dimensional Cellular automata Sadi, Nassima Ait Chemlal, Rezki Dynamical Systems Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both topological and ergodic point of view. The main results of the paper show the impossibility for a cellular automaton with a fully blocking pattern to have a measurable irrational eigenvalues. Further more, a cellular automaton with a set of equicontinuity points of positive measure cannot have a measurable irrational eigenvalue. |
| title | Irrational eigenvalues of D-Dimensional Cellular automata |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.00933 |