Normal forms for certain singularities of vectorfields

Floris Takens

Annales de l'institut Fourier (1973)

  • Volume: 23, Issue: 2, page 163-195
  • ISSN: 0373-0956

Abstract

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C normal forms are given for singularities of C vectorfields on R , which are not flat, and for C vectorfields X on R 2 with X ( 0 ) = 0 , the 1-jet of X in the origin is a pure rotation, and some higher order jet of X attracting or expanding.

How to cite

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Takens, Floris. "Normal forms for certain singularities of vectorfields." Annales de l'institut Fourier 23.2 (1973): 163-195. <http://eudml.org/doc/74122>.

@article{Takens1973,
abstract = {$C^\infty $ normal forms are given for singularities of $C^\infty $ vectorfields on $\{\bf R\}$, which are not flat, and for $C^\infty $ vectorfields $X$ on $\{\bf R\}^2$ with $X(0)=0$, the 1-jet of $X$ in the origin is a pure rotation, and some higher order jet of $X$ attracting or expanding.},
author = {Takens, Floris},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {163-195},
publisher = {Association des Annales de l'Institut Fourier},
title = {Normal forms for certain singularities of vectorfields},
url = {http://eudml.org/doc/74122},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Takens, Floris
TI - Normal forms for certain singularities of vectorfields
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 2
SP - 163
EP - 195
AB - $C^\infty $ normal forms are given for singularities of $C^\infty $ vectorfields on ${\bf R}$, which are not flat, and for $C^\infty $ vectorfields $X$ on ${\bf R}^2$ with $X(0)=0$, the 1-jet of $X$ in the origin is a pure rotation, and some higher order jet of $X$ attracting or expanding.
LA - eng
UR - http://eudml.org/doc/74122
ER -

References

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  1. [1] J. DIEUDONNÉ, Foundations of Modern Analysis, Acad. Press, New York, 1960. Zbl0100.04201MR22 #11074
  2. [2] S. KOBAYASHI and K. NOMIZU, Foundations of differential geometry vol. 1, Interscience, New York, 1963. Zbl0119.37502MR27 #2945
  3. [3] R. NARASIMHAN, Analysis on real and complex manifolds, North-Holland, Amsterdam, 1968. Zbl0188.25803MR40 #4972
  4. [4] S. STERNBERG, Local contractions and a theorem of Poincaré, Amer. J. Math. vol. LXXIX (1957), 809-824. Zbl0080.29902MR20 #3335
  5. [5] F. TAKENS, Singularities of vectorfields, to appear in Publ. I. H. E. S.. Zbl0279.58009
  6. [6] F. TAKENS, Derivations of vectorfields, to appear in Comp. Math.. Zbl0258.58005

Citations in EuDML Documents

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  1. Tomohiko Ishida, Second cohomology classes of the group of C 1 -flat diffeomorphisms
  2. Sergey Yu. Yakovenko, Smooth normalization of a vector field near a semistable limit cycle
  3. Hélène Eynard-Bontemps, Centralisateurs des difféomorphismes de la demi-droite
  4. S. Sergio Plaza, Global stability of saddle-node bifurcation of a periodic orbit for vector fields
  5. F. Dumortier, Robert Roussarie, Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilité finie
  6. Sergio Plaza, Jaime Vera, Bifurcation and stability of families of hyperbolic vector fields in dimension three
  7. Étienne Ghys, Takashi Tsuboi, Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1
  8. Christian Bonatti, Sebastião Firmo, Feuilles compactes d’un feuilletage générique en codimension 1
  9. Sheldon E. Newhouse, Jacob Palis, Floris Takens, Bifurcations and stability of families of diffeomorphisms
  10. Takashi Tsuboi, On 2-cycles of B Diff ( S 1 ) which are represented by foliated S 1 -bundles over T 2

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