CRM: Centro De Giorgi
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Renormalization small divisors continued fractions and geodesic flows

seminar: On the quasianalyticity properties of spaces of monogenic functions suitable for one-dimensional small divisor problems

speaker: David Sauzin (CNRS)

abstract: This is a joint work with Prof. Stefano Marmi

We discuss the quasianalytic properties of various spaces of functions suitable for one-dimensional small divisor problems, in the spirit of M.Herman's work on the linearization of the diffeomorphisms of the circle. Our spaces are formed of functions which are monogenic in the sense of E.Borel: they are $C1$-holomorphic (in the Whitney sense) on certain compact sets~$Kj$ of the Riemann sphere, as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of~$Kj$ with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity; in the case of the circle diffeomorphisms, the multiplier is related to the rotation number via the exponential map). It turns out that a kind of generalized analytic continuation through the unit circle is possible under suitable conditions on the $Kj$'s.

Thu 19 Apr, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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