Stability and Chaotic Dynamics in a Nonlinearly Confined ghost-sector Hamiltonian
We investigate the nonlinear dynamics of a Hamiltonian system containing a ghost degree of freedom coupled to a canonical sector through nonlinear interactions. The model consists of one positive-energy and one negative-energy mode, augmented by quartic and sextic nonlinearities that regularize the large-amplitude behavior of the system. Unlike conventional ghost models, which typically exhibit runaway trajectories due to the indefinite nature of the kinetic energy, the present Hamiltonian possesses a confining nonlinear structure that renders the accessible energy surfaces compact for finite total energy. We derive the equations of motion and analyze the geometric properties of the Hamiltonian flow. Particular attention is devoted to the interplay between local ghost-induced instability and global nonlinear confinement. We show that the sextic contribution dominates the asymptotic dynamics and prevents escape to infinity despite the presence of a negative-energy sector. As a consequence, the model provides a controlled framework for studying bounded dynamics in ghost-coupled systems. The phase-space structure is investigated through numerical integration, Poincaré surfaces of section, and Lyapunov analysis. Depending on the interaction strength and nonlinear couplings, the system exhibits a transition from regular quasi-periodic motion to chaotic dynamics characterized by positive maximal Lyapunov exponents. Remarkably, chaotic trajectories remain confined within compact regions of phase space, yielding a realization of bounded chaotic motion in a ghost-containing Hamiltonian system. These results provide a concrete example of how nonlinear self-interactions can regularize ghost dynamics at the classical level and indicate a useful prototype for studying stability, confinement, and chaos in nonstandard Hamiltonian theories.