Geometry and Dynamics of the Besicovitch and Weyl Spaces

Details Geometry and Dynamics of the Besicovitch and Weyl Spaces Geometry and Dynamics of the Besicovitch and Weyl Spaces

2012-04-24

arxiv.org/abs/1204.5371v1

Mathematics

Dynamical Systems

15 pages. Submitted to DLT 2012

Scientific paper

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.

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