# 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

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- [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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