Phys. Rev. E 49, 5717–5721 (1994)Parametric resonances in synchrotrons with two rf systemsReceived 6 March 1994; published in the issue dated June 1994 When a double rf system is subjected to sinusoidal phase modulation, the Poincaré surfaces of the section display a rich spectrum of resonance islands. Stable and unstable fixed points of these resonance islands form a tree of bifurcation branches which can be explained as parametric resonances generated by external phase modulation. A semianalytic determination of the condition for the bifurcation of fixed points is presented for an autonomous Hamiltonian of one degree of freedom with sinusoidal time dependent perturbation. © 1994 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.49.5717
DOI:
10.1103/PhysRevE.49.5717
PACS:
41.75.-i, 03.20.+i, 05.45.+b, 29.20.Dh
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