Identifiant pérenne de la notice : 208010386
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Note publique d'information : The authors consider applications of singularity theory and computer algebra to bifurcations
of Hamiltonian dynamical systems. They restrict themselves to the case were the following
simplification is possible. Near the equilibrium or (quasi-) periodic solution under
consideration the linear part allows approximation by a normalized Hamiltonian system
with a torus symmetry. It is assumed that reduction by this symmetry leads to a system
with one degree of freedom. The volume focuses on two such reduction methods, the
planar reduction (or polar coordinates) method and the reduction by the energy momentum
mapping. The one-degree-of-freedom system then is tackled by singularity theory, where
computer algebra, in particular, Gröbner basis techniques, are applied. The readership
addressed consists of advanced graduate students and researchers in dynamical systems.
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