This paper defines flows (or discrete dynamical systems) and cyclic flows in a category and investigates how the trajectories of a point might approach a cycle. The paper considers cyclic flows in the categories of Sets and of Boolean algebras and their duals and characterizes the Stone representation of a cyclic flow in Boolean algebras. A cyclic spectrum is constructed for Boolean flows. Examples include attractive fixpoints, repulsive fixpoints, strange attractors and the logistic equation.
Keywords: flow, discrete dynamical system, topos, Cole spectrum, strange attractor.
2000 MSC: 18B25, 37B99.
Theory and Applications of Categories, Vol. 10, 2002, No. 15, pp 392-409.