Linear Finite Dynamical Systems

ABSTRACT A Linear Finite Dynamical System (LFDS) is a pair (E, f) where E is a finite dimensional space over a finite field k. A complete description of the dynamics of f, the behavior of f's iterates, is given, based on the natural decomposition of any linear map into a nilpotent and bijective components. The results can be used for studying the dynamics of any linear map.