Hamiltonian Vector Field for the Lorenz Invariant Set

The existence of a Hamiltonian vector field in which trajectories of the invariant set of a dissipative hyperbolic chaotic system are embedded will be proved (see notation below). Evidence of this with an example concerning the Lorenz system will be provided. Also, a constructive method of designing a Hamiltonian for the Lorenz attractor with a universal approximator will be introduced. The present approach enables the use of the universal approximator property of neural networks for modeling dynamics from the Hamiltonian perspective. 1. Introduction Recent decades in the scientific literature brought much attention to the physics of low-dimensional chaos. In many technical applications, such as communication systems, ergodicity and continuous spectrum of chaotic signals became important and desired features. Frequently, numerical evaluation of chaotic maps or simple integration of a system's differential equations are sufficient means in attempted designs. Oftentimes, however, the p..