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Geometry and Dynamics of the Besicovitch and Weyl Spaces (1204.5371v1)
Published 24 Apr 2012 in math.DS, cs.DM, cs.FL, and math.AT
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 canonical projections into subshifts, characterize the cellular automata that are contracting or isometric in the Besicovitch or Weyl spaces, 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.