01093nas a2200145   4500008004100000245009200041210006900133300001300202490000800215520058600223100002100809700002300830700002400853856007000877       2018                        eng d00aSymplectic invariants for parabolic orbits and cusp singularities of integrable systems0 aSymplectic invariants for parabolic orbits and cusp singularitie  a201704240 v3763 a<p>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 article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.</p>1 aBolsinov, Alexey1 aGuglielmi, Lorenzo1 aKudryavtseva, Elena  uhttps://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424