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.

Keywords:

• Cycles
• Finite dynamical systems
• Graph of a map
• Trees

Mathematics Subject Classification:

• Primary 37B99
• Secondary 05C38
• 99B20
• 94C99

ACKNOWLEDGMENT

I would like to thank the anonymous referee of a previous version of this article, for pointing out to me the references about works in the area of electrical circuits.

Notes

^#Communicated by C. Cibils.