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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 4-5, Pages 781–804
DOI: https://doi.org/10.1134/S1560354723040160 (Mi rcd1233) 		 
This article is cited in 4 scientific papers (total in 5 papers)

Special Issue: On the 80th birthday of professor A. Chenciner

Normalization Flow

Dmitry V. Treschev

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991 Moscow, Russia
Citations (5)
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DOI: https://doi.org/10.1134/S1560354723040160
Abstract: We propose a new approach to the theory of normal forms for Hamiltonian systems near a nonresonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a differential equation in this space. Solutions of this equation move Hamiltonian functions towards their normal forms. Shifts along the flow of this equation correspond to canonical coordinate changes. So, we have a continuous normalization procedure. The formal aspect of the theory presents no difficulties. As usual, the analytic aspect and the problems of convergence of series are nontrivial.
Keywords: normal forms, Hamiltonian systems, small divisors.
Funding agency Grant number
Russian Science Foundation 20-11-20141
This work was supported by the Russian Science Foundation under grant no. 20-11-20141, https://rscf.ru/en/project/20-11-20141/.
Received: 02.08.2023
Accepted: 08.09.2023
Bibliographic databases:
Document Type: Article
MSC: 37J40, 34C20
Language: English
Citation: Dmitry V. Treschev, “Normalization Flow”, Regul. Chaotic Dyn., 28:4-5 (2023), 781–804
Citation in format AMSBIB
\Bibitem{Tre23}
\by Dmitry V. Treschev
\paper Normalization Flow
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 781--804
\mathnet{http://mi.mathnet.ru/rcd1233}
\crossref{https://doi.org/10.1134/S1560354723040160}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4658648}
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  • https://www.mathnet.ru/eng/rcd1233
  • https://www.mathnet.ru/eng/rcd/v28/i4/p781
    • This publication is cited in the following 5 articles:
    1. D. V. Treschev, “Normalization flow in the presence of a resonance”, Izv. RAN. Ser. matem., 89:1 (2025), 184–207  mathnet  crossref
    2. S. V. Bolotin, O. E. Zubelevich, V. V. Kozlov, S. B. Kuksin, A. I. Neishtadt, “Dmitrii Valerevich Treschev (k shestidesyatiletiyu so dnya rozhdeniya)”, UMN, 80:1(481) (2025), 165–170  mathnet  crossref
    3. D. V. Treschev, “Normalization flow in the presence of a resonance”, Izv. Math., 89:1 (2025), 172–195  mathnet  mathnet  crossref  crossref
    4. D. V. Treschev, E. I. Kugushev, T. V. Popova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskii, “Kafedra teoreticheskoi mekhaniki i mekhatroniki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 103–113  mathnet  crossref  elib
    5. D. V. Treschev, E. I. Kugushev, T. V. Shakhova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskiy, “Chair of Theoretical Mechanics and Mechatronics”, Moscow Univ. Mech. Bull., 79:6 (2024), 200  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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