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TMF, 1990, Volume 82, Number 2, Pages 268–277 (Mi tmf5415)  

Instability criterion for multidimensional nonlinear Hamiltonian systems

I. V. Krivoshei


Abstract: A differential-geometrical approach is proposed for the investigation of instability in multidimensional nonlinear conservative systems. The critical value $E_c$ of the total energy for onset of instability of the motion in the two-dimensional case is calculated as the smallest value of the potential $U(x,y)$ on the line of zero curvature $K(x,y)=0$ of the potential-energy surface: $E_c=\min U(x,y\mid K=0)$. The criterion is generalized to the multidimensional case and illustrated by definite examples of the Hènon–Heiles systems and the reduced three-dimensional Yang–Mills problem.

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English version:
Theoretical and Mathematical Physics, 1990, 82:2, 187–194

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Received: 17.05.1988

Citation: I. V. Krivoshei, “Instability criterion for multidimensional nonlinear Hamiltonian systems”, TMF, 82:2 (1990), 268–277; Theoret. and Math. Phys., 82:2 (1990), 187–194

Citation in format AMSBIB
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\by I.~V.~Krivoshei
\paper Instability criterion for multidimensional nonlinear Hamiltonian systems
\jour TMF
\yr 1990
\vol 82
\issue 2
\pages 268--277
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1048120}
\zmath{https://zbmath.org/?q=an:0705.53043}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 82
\issue 2
\pages 187--194
\crossref{https://doi.org/10.1007/BF01079047}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990DZ44000010}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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