INTEGRABLE ANALYTIC VECTOR-FIELDS WITH A NILPOTENT LINEAR PART

Authors
GONG XH
Citation
Xh. Gong, INTEGRABLE ANALYTIC VECTOR-FIELDS WITH A NILPOTENT LINEAR PART, Annales de l'Institut Fourier, 45(5), 1995, pp. 1449
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Annales de l'Institut Fourier → ACNP
ISSN journal
03730956
Volume
45
Issue
5
Year of publication
1995
Database
ISI
SICI code
0373-0956(1995)45:5<1449:IAVWAN>2.0.ZU;2-X
Abstract
We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transf ormed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly li nearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.