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Regular and Chaotic Dynamics, 2021, Volume 26, Issue 6, Pages 732–741
DOI: https://doi.org/10.1134/S1560354721060101
(Mi rcd1142)
 

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
Citations (7)
References:
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.
Funding agency Grant number
Russian Science Foundation 17-11-01303
The work of E. K. was supported by the Russian Science Foundation (grant No. 17-11-01303).
Received: 08.06.2021
Accepted: 20.10.2021
Bibliographic databases:
Document Type: Article
Language: English
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
Citation in format AMSBIB
\Bibitem{KudMar21}
\by Elena A. Kudryavtseva, Nikolay N. Martynchuk
\paper Existence of a Smooth Hamiltonian Circle Action
near Parabolic Orbits and Cuspidal Tori
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 6
\pages 732--741
\mathnet{http://mi.mathnet.ru/rcd1142}
\crossref{https://doi.org/10.1134/S1560354721060101}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85118690794}
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  • https://www.mathnet.ru/eng/rcd/v26/i6/p732
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:86
    References:12
     
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