Hamiltonian vector field for the Lorenz invariant set

The existence of a Hamiltonian vector field in which trajectories of the invariant set Λ of a dissipative hyperbolic chaotic system are embedded, is proved. This evidence with an example concerning the Lorenz system is provided. Also, a constructive method of designing a Hamiltonian for the Lorenz attractor with a universal approximator is introduced. The present approach enables the use of universal approximator property of neural networks for modeling dynamics from the Hamiltonian perspective