Non-integrability of the 1:1:2–resonance
1984 ◽
Vol 4
(4)
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pp. 553-568
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Keyword(s):
AbstractA Hamiltonian system of n degrees of freedom, defined by the function F, with an equilibrium point at the origin, is called formally integrable if there exist A A formal power series , functionally independent, in involution, and such that the Taylor expansion of F is a formal power series in the .Take n = 3, , F(k) homogeneous of degree k, F(2) > 0 and the eigenfrequencies in ratio 1:1:2. If F(3) avoids a certain hypersurface of ‘symmetric’ third order terms, then the F system is not formally integrable. If F(3) is symmetric but F(4) is in a non-void open subset, then homoclinic intersection with Devaney spiralling occurs; the angle decays of order 1 when approaching the origin.
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1992 ◽
Vol 44
(1)
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pp. 194-205
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Keyword(s):
2003 ◽
Vol 184
(2)
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pp. 369-383
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2004 ◽
Vol 339
(8)
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pp. 533-538
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2002 ◽
Vol 51
(3)
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pp. 403-410
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2017 ◽
Vol 2018
(15)
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pp. 4780-4798
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