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

Abstract

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.

arXiv comment3 figures

References in corpus (3)

• Symplectic invariants for parabolic orbits and cusp singularities of integrable systems with two degrees of freedom
• The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows
• (Vanishing) Twist in the Saddle-Centre and Period-Doubling Bifurcation

Cited by in corpus (6)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems
• Symplectic invariants for parabolic orbits and cusp singularities of integrable systems with two degrees of freedom
• Hidden toric symmetry and structural stability of singularities in integrable systems
• Existence of a smooth Hamiltonian circle action near parabolic orbits
• Constructions of b-semitoric systems
• Singular fibers of the Gelfand--Cetlin system on $\mathfrak{u}(n{)}^{\ast }$