DETERMINING STEADY STATE BEHAVIOUR OF DISCRETE MONOMIAL DYNAMICAL SYSTEMS

摘要

In previous work [3] Colon-Reyes et al developed criteria for determining when a discrete monomial dynamical system reaches steady state behaviour. These criteria depend on determining when a certain matrix over a finite ring, that is not a field, de fines a fixed point system. It was not until recently that criteria to determine linear steady state behaviour over rings have been found. Using these new results we present a new algorithm to determine steady state behaviour of monomial dynamical systems over finite fields. Delgado-Eckert [5] has also obtained an algorithm for the finite field case, but his algorithm does not take into account the result in [3] and requires O (n(4) q(2) log q) integer operations. Our algorithm requires only O (n(3) log(n log q)) integer operations.