1999
DOI: 10.1088/0951-7715/12/5/309
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Stability of equilibria and fixed points of conservative systems

Abstract: We consider the stability and instability of an equilibrium point of a Hamiltonian system of two degrees of freedom in certain resonance cases. We also consider the stability or instability of a fixed point of an area-preserving mapping in certain resonance cases. The stability criteria are established by Moser's invariant curve theorem and the instability is established by Chetaev's theorem.

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Cited by 41 publications
(43 citation statements)
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“…The fixed point is stable if |a 32 | > |a 05 | [24]. At the point in Table 1 where ω = 1/6, we find a 3,2 = i31 √ 3/72 while the resonant term a 0,5 = i13 √ 3/72 is much smaller; thus this point is stable [24].…”
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confidence: 69%
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“…The fixed point is stable if |a 32 | > |a 05 | [24]. At the point in Table 1 where ω = 1/6, we find a 3,2 = i31 √ 3/72 while the resonant term a 0,5 = i13 √ 3/72 is much smaller; thus this point is stable [24].…”
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confidence: 69%
“…The map is unstable when τ 0 = 0, providing a 0,n−1 = 0 [15,24]. For the cases in Table 1 with τ 0 = 0 we find: when ω = 1/4 a 0,3 = −i4/3, and when ω = 1/5, 2/5 we find a 0,…”
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confidence: 79%
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“…Markeev [17,18], Sokolsky [24,25,26]), where specific resonances are treated. Recently, Cabral and Meyer [6] revisited the problem and gave a general result that applies for both non-resonant and resonant cases.…”
Section: Introductionmentioning
confidence: 99%