Covering space in the Weyl and Besicovitch topologies

Covering Space in the Besicovitch Topology

This paper studies how one can spread points in the Besicovitch space in order to keep them far one from another. We first study the general case and then what happens if the chosen points are all regular Toeplitz configurations or all quasiperiodic configurations.

Cellular Automata in the Cantor, Besicovitch, and Weyl Topological Spaces

The Besicovitch and Weyl pseudometrics on the space AŸ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from A by factoring through the equivalence of zero distance. Cellular automata are considered as dynamical systems on the Besicovitch and Weyl spaces and their topological a...

Geometry and Dynamics of the Besicovitch and Weyl Spaces

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 automat...

Periodicity and Transitivity for Cellular Automata in Besicovitch Topologies

We study cellular automata (CA) behavior in Besicovitch topology. We solve an open problem about the existence of transitive CA. The proof of this result has some interest in its own since it is obtained by using Kolmogorov complexity. At our knowledge it if the first result on discrete dynamical systems obtained using Kolmogorov complexity. We also prove that every CA (in Besicovitch topology)...

On the sensitivity of additive cellular automata in Besicovitch topologies