Parametric Stabilization of Hierarchical Triple Systems: High-Frequency Floquet Dressing of Secular Resonances in Model Configurations

This work presents a theoretical framework for the stabilization of hierarchical triple systems under high-frequency parametric forcing. Using the secular Kozai-Lidov Hamiltonian, we analyze the effect of a fast, zero-mean oscillatory perturbation on long-term orbital dynamics via Floquet averaging techniques. We show that high-frequency driving induces a renormalization of the effective coupling constant governing eccentricity-inclination exchange, leading to a strong suppression of resonant excitation. This parametric modification restricts eccentricity growth and promotes a transition toward a dynamically stabilized orbital regime in model configurations. The results suggest that high-frequency perturbations may influence the stability of hierarchical N-body systems by modulating secular resonances within a non-equilibrium framework.