HAL : hal-00150953, version 1

arXiv : 0706.0138

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A quasianalyticity property for monogenic solutions of small divisor problems

Stefano Marmi 2, David Sauzin 1

(01/06/2007)

We discuss the quasianalytic properties of various spaces of functions suitable for one-dimensional small divisor problems. These spaces are formed of functions C^1-holomorphic on certain compact sets K_j of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of K_j with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is possible under suitable conditions on the K_j's.

1 :	Institut de Mecanique Celeste et de Calcul des Ephemerides (IMCCE)
	CNRS : UMR8028 – INSU – Observatoire de Paris – Université Pierre et Marie Curie - Paris VI
2 :	Gruppo di ricerca di sistemi dinamici (SNS PISA)
	Scuola Normale Superiore

Domaine

:

Mathématiques/Systèmes dynamiques

Mots Clés : Borel's monogenic functions – quasianalyticity – small divisors

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Contributeur : David Sauzin <>

Soumis le : Vendredi 1 Juin 2007, 10:53:36

Dernière modification le : Vendredi 1 Juin 2007, 14:08:11