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

TL;DR

This paper studies symplectic invariants and normal forms of parabolic orbits and cusp singularities in 2-degree-of-freedom integrable systems, introducing new techniques for analyzing degenerate singularities in geometry and physics.

Contribution

It provides a detailed analysis of symplectic invariants for specific degenerate singularities and proposes novel methods applicable to more complex degenerate cases.

Findings

Characterization of symplectic invariants for parabolic orbits

Development of new techniques for degenerate singularities

Application to integrable systems in geometry and physics

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.