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Regimes of stability of accelerator modes

Rebecca Hihinashvili·Tali Oliker·Yaniv S. Avizrats·Alexander Iomin·Shmuel Fishman·Italo Guarneri
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Abstract

The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions in the phase diagrams, which are analogous to the Arnol'd tongues which have been extensively studied for a variety of dynamical systems, mostly dissipative ones. A rich variety of bifurcations of various types are observed, as well as period doubling cascades. Stability of periodic orbits is analyzed in detail.

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Rebecca Hihinashvili, Tali Oliker, Yaniv S. Avizrats, Alexander Iomin, Shmuel Fishman, Italo Guarneri. 2006-04-02. Regimes of stability of accelerator modes. https://doi.org/10.1016/j.physd.2006.10.008

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