Existence of a smooth Hamiltonian circle action near parabolic orbits and cuspidal toriстатьяИсследовательская статья
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Дата последнего поиска статьи во внешних источниках: 12 января 2022 г.
Аннотация:We show that every parabolic orbit of a two-degree of freedom integrable system admits a C^1-smooth Hamiltonian circle action, which is persistent under small integrable C^1 perturbations. We deduce from this result the structural stability of parabolic orbits and show that they are all smoothly equivalent (in the non-symplectic sense) to a standard model. As a corollary, we obtain similar results for cuspidal tori. Our proof is based on showing that every symplectomorphism of a neighbourhood of a parabolic point preserving the first integrals of motion is Hamiltonian whose generating function is smooth and constant on the connected components of the common level sets.