Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0997.37017
Carletti, Timoteo; Marmi, S.
Linearization of analytic and non-analytic germs of diffeomorphisms of $(\Bbb C,0)$. (English)
[J] Bull. Soc. Math. Fr. 128, No.1, 69-85 (2000). ISSN 0037-9484

The authors study Siegel's center problem on the linearization of germs of diffeomorphisms in one complex variable. They first study the cases when the linearization operator is formal or analytic, and then give sufficient conditions for this operator to belong to a certain algebra of ultradifferentiable functions that includes the Gevrey functions. In the analytic case they give a direct proof (not using renormalization) of {\it J.-C. Yoccoz}'s result [Small divisors in dimension one (French), Astérisque 231, 3-88 (1995; Zbl 0836.30001)] on the optimality of the estimates obtained using the majorant series method. In the ultradifferentiable case they show that Bryuno's generalization of the Diophantine condition is sufficient for the linearization to belong to the same class as the germ. If the linearization is less regular than the germ, the authors obtain new conditions weaker than the Bryuno condition.
[Jeffrey S.Joel (Kelly)]

MSC 2000:: *37F50 Small divisors, rotation domains and linearization
37F25 Renormalization
37G05 Normal forms
30C99 Geometric function theory

Keywords: Siegel center problem; linearization; normal forms; analytic diffeomorphisms; Gevrey classes; small divisors

Citations: Zbl 0836.30001

Cited in: Zbl 1175.37050

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]