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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 1, Pages 209–233 (Mi izv2294)  

On the reduction to canonical form of a dynamical system in the neighborhood of a smooth invariant torus

A. M. Samoilenko


Abstract: We construct an iterative process for determining a transformation that transforms a given dynamical system in the vicinity of a smooth torus to canonical form. Necessary conditions (and also sufficient conditions) for reducibility are given.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:1, 211–234

Bibliographic databases:

UDC: 517.9
MSC: 34C35, 34C30
Received: 27.01.1970

Citation: A. M. Samoilenko, “On the reduction to canonical form of a dynamical system in the neighborhood of a smooth invariant torus”, Izv. Akad. Nauk SSSR Ser. Mat., 36:1 (1972), 209–233; Math. USSR-Izv., 6:1 (1972), 211–234

Citation in format AMSBIB
\Bibitem{Sam72}
\by A.~M.~Samoilenko
\paper On the reduction to canonical form of a~dynamical system in the neighborhood of a~smooth invariant torus
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 1
\pages 209--233
\mathnet{http://mi.mathnet.ru/izv2294}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=294815}
\zmath{https://zbmath.org/?q=an:0309.34031}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 1
\pages 211--234
\crossref{https://doi.org/10.1070/IM1972v006n01ABEH001871}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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