  In circular accelerators, crossing the linear coupling resonance induces the
exchange of the transverse emittances, provided the process is adiabatic. This
has been considered in some previous works, where the description of the
phenomenon has been laid down, and, more recently, where a possible explanation
of the numerical results has been proposed. In this paper, we introduce a
theoretical framework to analyze the crossing process, based on the theory of
adiabatic invariance for Hamiltonian mechanics, which explains in detail
various features of the emittance exchange process.
