REGULAR ARTICLES Twist singularities for symplectic maps
نویسندگان
چکیده
Near a nonresonant, elliptic fixed point, a symplectic map can be transformed into Birkhoff normal form. In these coordinates, the dynamics is represented entirely by the Lagrangian ‘‘frequency map’’ that gives the rotation number as a function of the action. The twist matrix, given by the Jacobian of the rotation number, describes the anharmonicity in the system. When the twist is singular the frequency map need not be locally one-to-one. Here we investigate the occurrence of fold and cusp singularities in the frequency map. We show that folds necessarily occur near third order resonances. We illustrate the results by numerical computations of frequency maps for a quadratic, symplectic map. © 2003 American Institute of Physics. @DOI: 10.1063/1.1529450#
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