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.
Piecewise linear periodic maps of the plane with integer coefficients
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abstract
We study periodic, piecewise linear maps on the plane starting with the Mort Brown's map. We show that if the number of pieces is two, there is only a short list of possible periods (this fact can be seen as the crystallographic restriction for this class of maps). Otherwise, without the restriction on the number of pieces, a map can have any period. We show how to construct such maps using binary trees and so called admissible sequences.
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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.