Geometry and Dynamics of the Besicovitch and Weyl Spaces
Dynamical Systems
2012-04-25 v1 Discrete Mathematics
Formal Languages and Automata Theory
Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1204.5371,
title = {Geometry and Dynamics of the Besicovitch and Weyl Spaces},
author = {Ville Salo and Ilkka Törmä},
journal= {arXiv preprint arXiv:1204.5371},
year = {2012}
}
Comments
15 pages. Submitted to DLT 2012