Singularity theory or catastrophe theory has been attracting researcher for
more than half a century. Nowadays, a well-developed framework is available
to analyse which bifurcations occur in gradient-zero-problems for families
of smooth scalar valued map germs. In this talk I will introduce a geometric
picture involving the intersection of Lagrangian submanifolds to analyse how
and to which extend boundary value problems in Hamiltonian systems fit into
the framework of singularity theory. Moreover, I will analyse how conserved
quantities and symmetries lead to new bifurcation phenomena. |