(Preprint) AAS 12-629 USING CARLEMAN EMBEDDING TO DISCOVER A SYSTEM’S MOTION CONSTANTS

Although the solutions with respect to time are commonly sought when analyzing the behavior of dynamic systems, there are other expressions that can be as revealing and important. Specifically, motion constants, which are time independent algebraic or transcendental equations involving the system states, can provide a broad view of a system’s motion. Locally, at least, the motion constants of autonomous systems exist. Nevertheless, for finite dimensional, autonomous, nonlinear systems, the motion constants are generally difficult to identify. The motion constants for every finite dimensional, autonomous, linear system, regardless of its dimension, however, have recently been found. This paper attempts to discover the motion constants of nonlinear systems through the motion constants of a linear representation. The linear representation is achieved through a Carleman embedding, which provides a procedure to transform a finite dimensional system of analytic ordinary differential equations into an infinite system of linear differential equations