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math.SP2026
Elementary cellular automata: spectral properties of Koopman operator for finite periodic realizations
Qingying Zhu, Serge Richard
In this paper we study Koopman operators associated with finite periodic realizations of elementary cellular automata. The spectra of these operators encompass various properties o…
math.SP2026
Dirac operators on periodic planar graphs: the right definition advocated by flat bands
Koichi Kato, Daniel Parra, Serge Richard
Massive discrete Dirac-type operators on periodic planar graphs are investigated. Using Floquet--Bloch decomposition, we first show that neglecting the faces leads to spurious flat…