Factor maps between tiling dynamical systems

Details Factor maps between tiling dynamical systems Factor maps between tiling dynamical systems

1998-06-18

arxiv.org/abs/math/9806096v2

Forum Mathematicum 11 (1999), 503-512.

Mathematics

Dynamical Systems

8 pages

Scientific paper

We show that there is no Curtis-Hedlund-Lyndon Theorem for factor maps between tiling dynamical systems: there are codes between such systems which cannot be achieved by working within a finite window. By considering 1-dimensional tiling systems, which are the same as flows under functions on subshifts with finite alphabets of symbols, we construct a `simple' code which is not `local', a local code which is not simple, and a continuous code which is neither local nor simple.

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