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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 300, Pages 259–265 (Mi znsl1026)  
This article is cited in 1 scientific paper (total in 1 paper)

The Andronov–Hopf bifurcation with $2:1$ resonance

D. Yu. Volkov

Russian State Pedagogical University of Herzen, Department of Mathematics
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Abstract: We consider dissipative dynamical systems in the neighborhood of quasi-periodic $n$-dimensional invariant tori that are not normally hyperbolic. We assume that the normal spectrum contains precisely two pairs of simple pure imaginary eigenvalues. We investigate the case where the frequencies are in the ratio $2:1$. We establish sufficient conditions for the existence of invariant tori of dimension $n+p$ in certain region of the parameter space.
Received: 30.11.2002
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 128, Issue 2, Pages 2831–2834
DOI: https://doi.org/10.1007/s10958-005-0241-9
Bibliographic databases:
UDC: 517.925
Language: English
Citation: D. Yu. Volkov, “The Andronov–Hopf bifurcation with $2:1$ resonance”, Representation theory, dynamical systems. Part VIII, Special issue, Zap. Nauchn. Sem. POMI, 300, POMI, St. Petersburg, 2003, 259–265; J. Math. Sci. (N. Y.), 128:2 (2005), 2831–2834
Citation in format AMSBIB
\Bibitem{Vol03}
\by D.~Yu.~Volkov
\paper The Andronov--Hopf bifurcation with~$2:1$ resonance
\inbook Representation theory, dynamical systems. Part~VIII
\bookinfo Special issue
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 300
\pages 259--265
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1026}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1995367}
\zmath{https://zbmath.org/?q=an:1120.37030}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 2
\pages 2831--2834
\crossref{https://doi.org/10.1007/s10958-005-0241-9}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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