Perturbing a Symmetric Resonance: the Magnetic Spherical Pendulum
نویسنده
چکیده
We consider symmetric 2 degree of freedom Hamiltonian systems which are resonant because of the symmetry, such as the spherical pendulum. Perturbing such a system by breaking the symmetry (e.g. adding a magnetic term) creates bifur-cations in the geometry of the families of periodic orbits, and the aim of this paper is to study this geometry. For brevity, we consider only the cases of symmetry breaking O(2) ! SO(2) and D 4 ! Z 4. We follow the standard approach of Lyapounov-Schmidt reduction and normal form theory together with singular-ity theory to justify the truncation to normal form. However, the details of the singularity theory are new.
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