E. Shlizerman and V. Rom-Kedar,
Energy surfaces and Hierarchies of bifurcations - Instabilities in the forced truncated NLS

In Proceedings of the International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems. October, 2004.


A two-degrees of freedom near integrable Hamiltonian which arises in the study of low-amplitude near-resonance envelope solutions of the forced Sine-Gordon equation is analyzed. The energy momentum bifurcation diagrams and the Fomenko graphs are constructed and reveal the bifurcation values at which the lower dimensional model exhibits instabilities and non-regular orbits of a new type. Furthermore, this study leads to some new insights regarding the hierarchy of bifurcations appearing in integrable Hamiltonian systems and the role of global bifurcations in the energy momentum bifurcation diagrams.


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