# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Linearization of analytic and non-analytic germs of diffeomorphisms of $\left(ℂ,0\right)$. (English) Zbl 0997.37017
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 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.

##### MSC:
 37F50 Small divisors, rotation domains and linearization; Fatou and Julia sets 37F25 Renormalization 37G05 Normal forms 30C99 Geometric function theory