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Matematicheskie Zametki, 1974, Volume 16, Issue 3, Pages 407–414 (Mi mzm7475)  
This article is cited in 5 scientific papers (total in 5 papers)

Normal form of differential equations with a small parameter

A. D. Bruno

Applied Mathematics Institute, Academy of Sciences of the USSR
Full-text PDF (550 kB) Citations (5)
Abstract: In this paper we study a system of ordinary differential equations with a small parameter in the neighborhood of a fixed solution. We find a normal form for such a system. Then for the case of a small parameter and a single resonance we show that the formal integral manifold, found by V. I. Arnol'd (see Referativnyi Zhurnal Matematika, 8B678), is not always analytic. We discuss the conditions under which it is analytic.
Received: 18.12.1973
English version:
Mathematical Notes, 1974, Volume 16, Issue 3, Pages 832–836
DOI: https://doi.org/10.1007/BF01148130
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: A. D. Bruno, “Normal form of differential equations with a small parameter”, Mat. Zametki, 16:3 (1974), 407–414; Math. Notes, 16:3 (1974), 832–836
Citation in format AMSBIB
\Bibitem{Bru74}
\by A.~D.~Bruno
\paper Normal form of differential equations with a~small parameter
\jour Mat. Zametki
\yr 1974
\vol 16
\issue 3
\pages 407--414
\mathnet{http://mi.mathnet.ru/mzm7475}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=364763}
\zmath{https://zbmath.org/?q=an:0314.34043}
\transl
\jour Math. Notes
\yr 1974
\vol 16
\issue 3
\pages 832--836
\crossref{https://doi.org/10.1007/BF01148130}
Linking options:
  • https://www.mathnet.ru/eng/mzm7475
  • https://www.mathnet.ru/eng/mzm/v16/i3/p407
    • This publication is cited in the following 5 articles:
    1. Mikhail B. Mishustin, “On Foliations in Neighborhoods of Elliptic Curves”, Arnold Math J., 2:2 (2016), 195  crossref
    2. The Method of Normal Forms, 2011, 319  crossref
    3. Arnold's Problems, 2005, 181  crossref
    4. A. D. Bruno, “The normal form of a Hamiltonian system”, Russian Math. Surveys, 43:1 (1988), 25–66  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. I. Arnol'd, “Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves”, Funct. Anal. Appl., 10:4 (1976), 249–259  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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