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Zbl 1186.37057
Ribón, Javier
Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy. (English)
[J] Ann. Inst. Fourier 59, No. 3, 951-975 (2009). ISSN 0373-0956; ISSN 1777-5310/e

Let us denote {Diff}$(\mathbb{C}^n,0)$ the set of germs of complex analytic diffeomorphisms at $(\mathbb{C}^n,0)$ whereas $\widehat{\text{Diff}}(\mathbb{C}^n,0)$ is the formal completion of Diff$(\mathbb{C}^n,0)$. The formal class of a germ of diffeomorphism $\varphi$ is embeddable in a flow if $\varphi$ is formally conjugated to the exponential of a germ of vector field. The main theorem of this paper is: There exists a unipotent germ of complex analytic diffeomorphism at Diff$(\mathbb{C}^2,0)$ whose formal class is not embeddable.
[Alois Kl\'\ič (Praha)]

MSC 2000:: *37F75 Holomorphic foliations and vector fields
32H02 Holomorphic mappings on analytic spaces
32A05 Power series, etc. (several complex variables)
40A05 Convergence of series and sequences

Keywords: holomorphic dynamical systems; diffeomorphisms; vector fields; potential theory; infinitesimal generator; exponential map

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