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EnglishWe 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.
| Titolo: | There is only one KAM curve | |
| Autori: | ||
| Data di pubblicazione: | 2014 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/0951-7715/27/9/2035 | |
| Handle: | http://hdl.handle.net/11384/57280 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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