Geometry and dynamics of the besicovitch and weyl spaces

Authors:
Ville Salo;Ilkka Törmä
Affiliations:
TUCS --- Turku Centre for Computer Science, University of Turku, Finland;University of Turku, Finland
Venue:
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Year:
2012

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Abstract

We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition, we study continuous functions that locally look like cellular automata and present a new proof for the nonexistence of transitive cellular automata in the Besicovitch space.