Integrable analytic vector fields with a nilpotent linear part
Annales de l'institut Fourier (1995)
- Volume: 45, Issue: 5, page 1449-1470
- ISSN: 0373-0956
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topGong, Xianghong. "Integrable analytic vector fields with a nilpotent linear part." Annales de l'institut Fourier 45.5 (1995): 1449-1470. <http://eudml.org/doc/75166>.
@article{Gong1995,
abstract = {We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly linearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.},
author = {Gong, Xianghong},
journal = {Annales de l'institut Fourier},
keywords = {embeddability of mappings; normalization; analytic vector fields; nilpotent linear part; transformations},
language = {eng},
number = {5},
pages = {1449-1470},
publisher = {Association des Annales de l'Institut Fourier},
title = {Integrable analytic vector fields with a nilpotent linear part},
url = {http://eudml.org/doc/75166},
volume = {45},
year = {1995},
}
TY - JOUR
AU - Gong, Xianghong
TI - Integrable analytic vector fields with a nilpotent linear part
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 5
SP - 1449
EP - 1470
AB - We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly linearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.
LA - eng
KW - embeddability of mappings; normalization; analytic vector fields; nilpotent linear part; transformations
UR - http://eudml.org/doc/75166
ER -
References
top- [1] V.I. ARNOL'D and Yu. S. IL'YASHENKO, Ordinary differential equations, in “Dynamical Systems I, EMS” vol. 1, Springer-Verlag, Berlin, 1990. Zbl0789.53017
- [2] A. BAIDER and J. C. SANDERS, Further reduction of the Takens-Bogdanov normal form, J. Diff. Equations, 99 (1992), 205-244. Zbl0761.34027MR93m:58101
- [3] R.I. BOGDANOV, Versal deformation of a singularity of a vector field on the plane in the case of zero eigenvalues, Seminar Petrovski (1976), and Selecta Math. Soviet, n° 4, 1 (1981), 389-421. Zbl0518.58030
- [4] D. CERVEAU and R. MOUSSU, Groupes d'automorphismes de (C, 0) et équations différentielles y dy + ... = 0, Bull. Soc. Math. France, 116 (1988), 459-488. Zbl0696.58011MR90m:58192
- [5] X. GONG, Divergence for the normalization of real analytic glancing hypersurfaces, Commun. Partial Diff. Equations, 19, n° 3 & 4 (1994), 643-654. Zbl0804.53080MR95f:58079
- [6] R.B. MELROSE, Equivalence of glancing hypersurfaces, Invent. Math., 37 (1976), 165-191. Zbl0354.53033MR55 #9173
- [7] F. TAKENS, Singularities of vector fields, Publ. Math. I.H.E.S., 43 (1974), 47-100. Zbl0279.58009MR49 #4052
- [8] S.M. WEBSTER, Holomorphic symplectic normalization of a real function, Ann. Scuola Norm. Sup. di Pisa, 19 (1992), 69-86. Zbl0763.58010MR94d:32024
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