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This article is cited in 7 scientific papers (total in 7 papers)
Regular Papers
Existence of a Smooth Hamiltonian Circle Action
near Parabolic Orbits and Cuspidal Tori
Elena A. Kudryavtsevaab, Nikolay N. Martynchukca a Moscow Center of Fundamental and Applied Mathematics,
Leninskie Gory 1, 119991 Moscow, Russia
b Faculty of Mechanics and Mathematics, Moscow State University,
Leninskie Gory 1, 119991 Moscow, Russia
c Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence,
University of Groningen,
P.O. Box 407, 9700 AK Groningen, The Netherlands
Abstract:
We show that every parabolic orbit of a two-degree-of-freedom integrable system admits a $C^\infty$-smooth Hamiltonian
circle action, which is persistent under small integrable $C^\infty$ 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 a Hamiltonian whose generating function is smooth and constant on the
connected components of the common level sets.
Keywords:
Liouville integrability, parabolic orbit, circle action, structural stability, normal
forms.
Received: 08.06.2021 Accepted: 20.10.2021
Citation:
Elena A. Kudryavtseva, Nikolay N. Martynchuk, “Existence of a Smooth Hamiltonian Circle Action
near Parabolic Orbits and Cuspidal Tori”, Regul. Chaotic Dyn., 26:6 (2021), 732–741
Linking options:
https://www.mathnet.ru/eng/rcd1142 https://www.mathnet.ru/eng/rcd/v26/i6/p732
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Abstract page: | 86 | References: | 12 |
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