Effect of linear coupling on nonlinear resonances in betatron motion

The influence of linear coupling on nonlinear resonances in betatron motion is considered. A model of lattice with a single sextupole and a linearly coupled one-turn matrix is analyzed. The perturbative approach based on normal forms is considered, and the relation of the first resonant coefficient of the interpolating Hamiltonian with the island width or with the unstable separatrices is outlined. The dependence of the first resonant coefficient on the coupling angle is worked out for generic resonances. The analytical results are in very good agreement with the numerical simulations based on tracking and frequency analysis.