Mean-motion resonances give birth to surprisingly complex problems despite the relative simplicity of the physics underlain. Solutions can be represented in a straightforward way through Hamiltonian maps when the resonant angle is the only degree of freedom, but most physical perturbations introduce additional degrees of freedom. This is the case when the resonance is perturbed by an outer planet, whether eccentric or inclined. In this talk, I would like to present a theoretical study on the influence of an external planet misaligned with inner smaller resonant bodies, within the circular restricted problem. The behavior of the system depends on the relative strength between the coupling of the bodies and the perturbations from the outer planet. We demonstrated that mean-motion resonance strengthens the inner coupling and is very resilient to the perturbation, surviving periodic relative inclination increases of tens of degrees between the inner bodies.
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