Dynamics Seminar

Event Information Title: E pluribus unum: natural boundaries and uniqueness of KAM curves
Starts: 15:10 on Wednesday October 30, 2013
Ends: 16:00 on Wednesday October 30, 2013
Location: BA6180, Bahen Center, 40 St. George St.
Speaker: Stefano Marmi
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Institution: Scuola Normale Superiore di Pisa
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Abstract:

Addressing a question raised by Kolmogorov and Herman, we show that KAM curves of area-preserving twist maps are uniquely determined by their knowledge on a set of positive 1-dimensional Hausdorff measure in frequency space. This result is obtained by complexifying the rotation number and by an extension of the classical theory of quasianalytic functions.

Background material:

The parametrization of KAM curves is naturally defined in a complex domain containing the real Diophantine frequencies. Real frequencies constitute a natural boundary for the analytic continuation from the Weierstrass point of view because of the density of the resonances.