Eli Shlizerman and Vered Rom-Kedar
Energy surfaces and Hierarchies of bifurcations - Instabilities in the forced truncated NLS.
(773K, pdf)

ABSTRACT.  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 
\emph{hierarchy of bifurcations} appearing in integrable 
Hamiltonian systems and the role of global bifurcations in the 
energy momentum bifurcation diagrams.