Some Spectral Properties of One Dimensional Cellular Automata
In this paper we consider one-dimensional cellular automata. We investigate the possibility for a cellular automaton to have irrational eigenvalues in both topological and ergodic field.
We show that cellular automata with equicontinuous or almost equicontinuous points cannot have irrational measurable eigenvalues.
2000 Mathematics Subject Classification: 37B15, 54H20, 37A30.
Keywords: Cellular automata, dynamical systems, ergodic theory, eigenvalues.