Geodesic
Instability criterion for multidimensional nonlinear Hamiltonian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 2, pp. 268-277 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {I. V. Krivoshei},
     title = {Instability criterion for multidimensional nonlinear {Hamiltonian} systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {268--277},
     year = {1990},
     volume = {82},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_82_2_a9/}
}
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I. V. Krivoshei. Instability criterion for multidimensional nonlinear Hamiltonian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 2, pp. 268-277. http://geodesic.mathdoc.fr/item/TMF_1990_82_2_a9/

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