BOLSINOV, A.V., GUGLIELMI, L. and KUDRYAVTSEVA, E., 2018. Symplectic invariants for parabolic orbits and cusp singularities of integrable systems. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 376: 20170424.
We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example
of degenerate singularities. We also suggest some new techniques which apparently can be used for
studying symplectic invariants of degenerate singularities of more general type.
This paper was accepted for publication in the journal Philosophical Transactions A: Mathematical, Physical and Engineering Sciences and the definitive published version is available at https://doi.org/10.1098/rsta.2017.0424