Different mechanisms may couple the equations of betatron motion and synchrotron motion through the physical quantities of accelerators such as chromaticity and dispersion. They generate synchro-betatron resonances (SBR) that can be seen as sidebands of the pure betatron resonances. The importance of having convenient formulae to analyse their damaging effects, to make numerical evaluations, and to find possible corrections is emphasized. It is shown how the Hamiltonian formalism can be used to reach these goals. Direct applications to design studies or functioning accelerators are given, together with some observations.
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