Lasers, stability, and numbers

Can insight familiar from quantum physics be used to uncover unsuspected features of classical dynamical systems? Is it possible to discover signatures of familiar quantum concepts in the realm of classical dynamics? For the wide class of systems governed by polynomial equations of motion, this paper argues that the concept of entanglement has a purely classical analogon, illustrating the analogy analytically for two paradigmatic systems, in one and in two-dimensions. The analogy emerges from properties of simple equations of motion of lasers, by demonstrating that complete sets of periodic modes may be encoded into a single orbital equation, a mode carrier, which parameterizes the entire set. The open question of mode isomorphism is also briefly addressed in the context above. Carriers provide a fresh technique for tracking and controlling classical dynamical systems, putting the emphasis on the study of orbital equations instead of orbital points. (paper)