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We discuss normal forms and symplectic invariants of parabolic orbits andcuspidal tori in integrable Hamiltonian systems with two degrees of freedom.Such singularities appear in many integrable systems in geometry andmathematical physics and can be considered as the simplest example ofdegenerate singularities. We also suggest some new techniques which apparentlycan be used for studying symplectic invariants of degenerate singularities ofmore general type.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Symplectic invariants for parabolic orbits and cusp singularities of integrable systems with two degrees of freedom