Surjunctivity for cellular automata in Besicovitch spaces

Details Surjunctivity for cellular automata in Besicovitch spaces Surjunctivity for cellular automata in Besicovitch spaces

2007-05-04

arxiv.org/abs/0705.0670v3

Mathematics

Dynamical Systems

9 pages, no figures, LaTeX. Shortened, some definition changed, proof of main lemma changed accordingly. Almost as submitted t

Scientific paper

The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product topology; in particular, that injectivity still implies surjectivity.

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