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- W2046778097 abstract "According to a theorem of Moser, every monotone twist map $varphi$ on the cylinder ${Bbb S}^1times {Bbb R}$, which is integrable outside a compact set, is the time-1-map $varphi_H^1$ of a fibrewise convex Hamiltonian $H$. In this paper we prove that if this particular flow $varphi_H^t$ is also integrable outside a compact set, then $varphi$ has to be integrable on the whole cylinder (and vice versa , of course). From this dynamical point of view, integrable twist maps appear to be quite rigid. As is shown in the appendix, an analogous rigidity result becomes trivial in higher dimensions." @default.
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- W2046778097 date "1998-06-01" @default.
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- W2046778097 title "Rigidity of integrable twist maps and a theorem of Moser" @default.
- W2046778097 doi "https://doi.org/10.1017/s0143385798108179" @default.
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