Open Dimensional Dynamical Systems

The theme of this issue of Artiicial Life is that traditional Dynamical Systems theory is inadequate for many problems in the study of Complex Systems. In this paper, I argue that the nite dimensional nature of traditional dynamical systems is inappropriate for evolutionary systems, but that simply embedding the dynamics into an innnite dimensional space overly complicates the mathematics and obscures important features of the complex system. Instead, I believe a new branch of mathematics is needed, which I term open dimensional dynamical systems, systems whose dimensionality is nite at any point in time, but whose dimension varies through time.