Complex Differential 1-Form and the Hénon–Heiles Potential

Abstract

we constructed the family of Hénon–Heiles potentials under the condition that the real or imaginary parts of the complex differentiable 1-form do not satisfy the Poincaré lemma. We showed that the scalar Hénon–Heiles potential serves as the source of the vortex field circulation of the force applied to the test particle. We also showed that the circulation density of the vortex field of the force remains constant even within the region of chaotic or quasi-chaotic motion.