We consider the standard family of area-preserving twist maps of the annulus and the corresponding KAM curves. Addressing a question raised by Kolmogorov, we show that, instead of viewing these invariant curves as separate objects, each of which having its own Diophantine frequency, one can encode them in a single function of the frequency, which is naturally defined in a complex domain containing the real Diophantine frequencies and which is monogenic in the sense of Borel; this implies a remarkable property of quasianalyticity, a form of uniqueness of the monogenic continuation, although real frequencies constitute a natural boundary for the analytic continuation from the Weierstraß point of view because of the density of the resonances.
|Autori:||Carlo Carminati; Stefano Marmi; David Sauzin|
|Titolo:||There is only one KAM curve|
|Anno del prodotto:||2014|
|Digital Object Identifier (DOI):||10.1088/0951-7715/27/9/2035|
|Appare nelle tipologie:||1.1 Articolo in rivista|