The symmetric McMillan map with mixed nonlinearity reduces to two key parameters and yields exact action-angle variables with closed-form rotation number and nonlinear tune shift.
Michelotti, Intermediate Classical Dynamics with Applications to Beam Physics , Wiley Series in Beam Physics and Accelerator Technology (Wiley, 1995)
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Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity
The symmetric McMillan map with mixed nonlinearity reduces to two key parameters and yields exact action-angle variables with closed-form rotation number and nonlinear tune shift.