AI 中文总结
研究含鬼自由度与正则区耦合的哈密顿系统非线性动力学，通过推导方程、分析几何性质及数值研究相空间结构，发现系统能实现有界混沌运动，为研究非标准哈密顿理论相关特性提供有用原型。
AI 中文摘要
我们研究了一个哈密顿系统的非线性动力学，该系统包含一个通过非线性相互作用与正则区耦合的鬼自由度。该模型由一个正能量和一个负能量模式组成，并通过四次和六次非线性项增强，以规范系统的大振幅行为。与传统鬼模型不同，该哈密顿量具有约束非线性结构，使有限总能量下的可及能量面紧凑。我们推导了运动方程并分析了哈密顿流的几何性质，特别关注局部鬼诱导不稳定性和全局非线性约束之间的相互作用。结果表明六次项主导渐近动力学并防止逃逸到无穷大。通过数值积分、庞加莱截面和李雅普诺夫分析研究了相空间结构，系统展现了从规则准周期运动到具有正最大李雅普诺夫指数的混沌动力学的转变，混沌轨迹局限在相空间的紧凑区域内。这些结果提供了一个非线性自相互作用如何在经典水平上规范鬼动力学的具体例子，并为研究非标准哈密顿理论中的稳定性、约束和混沌提供了一个有用的原型。
英文摘要
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.
Comments13 pages, 6 figures
