Notes on Symbolic Representations of Dynamical Systems
In this note, we presents some discussions on symbolic representations of dynamical systems through shifts and subshifts. By employing the tool of symbolic dynamics, we show that there exists a conjugate representation between general symbolic dynamical systems and usual symbolic dynamical systems through subshifts. For any one-dimensional cellular automaton, we demonstrate that there exists a subsystem such that it is a semi-conjugate representation of the cellular automaton through the shift.
Keywords: Symbolic representation; cellular automaton; subshift; symbolic dynamics