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- W1989949376 abstract "The disappearance of KAM tori is studied on the non-integrable Hamiltonian H(x,v,t)=v2/2 − M cos x − P cos k(x − t). A first method, which is an approximate renormalization procedure, allows one to make a local description of the phase space. The stability of cycles is studied by means of a second method which involves a Mathieu equation. The compounding of the two methods allows one to compute analytically the residue R and the mean residue ƒ, first introduced by J. Greene. One recovers and analytically generalizes his main numerical conjectures about the link between KAM tori and nearby cycles. The existence of a mean residue is shown for almost all tori, in the sense of the Lebesgue measure. Critical residues are shown to be universal quantities, in accordance with results of S.J. Shenker and L.P. Kadanoff." @default.
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- W1989949376 date "1984-11-01" @default.
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- W1989949376 title "Destruction of KAM tori in Hamiltonian systems: Link with the destabilization of nearby cycles and calculation of residues" @default.
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- W1989949376 doi "https://doi.org/10.1016/0167-2789(84)90134-9" @default.
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