See here (local).

A symbolic dynamical system often results from the partitioning of the state space of a general Dynamical system.

See overleaf for a nice review I wrote (also in email to Ard)

chapter of nice book on applied symbolic dynamics and chaos

http://bactra.org/notebooks/symbolic-dynamics.html

http://bactra.org/notebooks/symbolic-dynamics.html

Sequence spaces

Shift space

https://en.wikipedia.org/wiki/Shift_space

http://www.math.harvard.edu/library/sternberg/slides/symbolic.pdf :

http://www.scholarpedia.org/article/Symbolic_dynamics

See Fractal, Complex systems