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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 322, Pages 38–57
DOI: https://doi.org/10.4213/tm4331 (Mi tm4331) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Separatrix Maps in Slow–Fast Hamiltonian Systems

Sergey V. Bolotin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (321 kB) Citations (3)
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DOI: https://doi.org/10.4213/tm4331
Abstract: We obtain explicit formulas for the separatrix map of a multidimensional slow–fast Hamiltonian system. This map is used to partly extend Neishtadt's results on the jumps of adiabatic invariants at the separatrix to the multidimensional case.
Keywords: slow–fast system, homoclinic orbit, Poincaré function, separatrix map, adiabatic invariant.
Received: January 20, 2023
Revised: February 20, 2023
Accepted: April 25, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 322, Pages 32–51
DOI: https://doi.org/10.1134/S0081543823040041
Bibliographic databases:
Document Type: Article
UDC: 517.928.7+517.933
Language: Russian
Citation: Sergey V. Bolotin, “Separatrix Maps in Slow–Fast Hamiltonian Systems”, Modern Methods of Mechanics, Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii, Trudy Mat. Inst. Steklova, 322, Steklov Math. Inst., Moscow, 2023, 38–57; Proc. Steklov Inst. Math., 322 (2023), 32–51
Citation in format AMSBIB
\Bibitem{Bol23}
\by Sergey~V.~Bolotin
\paper Separatrix Maps in Slow--Fast Hamiltonian Systems
\inbook Modern Methods of Mechanics
\bookinfo Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 322
\pages 38--57
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4331}
\crossref{https://doi.org/10.4213/tm4331}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 322
\pages 32--51
\crossref{https://doi.org/10.1134/S0081543823040041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85180167276}
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  • https://www.mathnet.ru/eng/tm4331
  • https://doi.org/10.4213/tm4331
  • https://www.mathnet.ru/eng/tm/v322/p38
    • This publication is cited in the following 3 articles:
    1. Sergey V. Bolotin, “Dynamics of Slow-Fast Hamiltonian Systems: The Saddle–Focus Case”, Regul. Chaotic Dyn., 30:1 (2025), 76–92  mathnet  crossref
    2. 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
    3. 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
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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