Local structural stability of C 2 integrable 1-forms

Alcides Lins Neto

Annales de l'institut Fourier (1977)

  • Volume: 27, Issue: 2, page 197-225
  • ISSN: 0373-0956

Abstract

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In this work we consider a class of germs of singularities of integrable 1-forms in R n which are structurally stable in class C r ( r ≥ 2 if n = 3 , r ≥ 4 if n ≥ 4 ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.

How to cite

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Neto, Alcides Lins. "Local structural stability of $C^2$ integrable 1-forms." Annales de l'institut Fourier 27.2 (1977): 197-225. <http://eudml.org/doc/74317>.

@article{Neto1977,
abstract = {In this work we consider a class of germs of singularities of integrable 1-forms in $R^n$ which are structurally stable in class $C^r$ ($r\ge 2$ if $n=3$, $r\ge 4$ if $n\ge 4$), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.},
author = {Neto, Alcides Lins},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {197-225},
publisher = {Association des Annales de l'Institut Fourier},
title = {Local structural stability of $C^2$ integrable 1-forms},
url = {http://eudml.org/doc/74317},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Neto, Alcides Lins
TI - Local structural stability of $C^2$ integrable 1-forms
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 2
SP - 197
EP - 225
AB - In this work we consider a class of germs of singularities of integrable 1-forms in $R^n$ which are structurally stable in class $C^r$ ($r\ge 2$ if $n=3$, $r\ge 4$ if $n\ge 4$), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.
LA - eng
UR - http://eudml.org/doc/74317
ER -

References

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  1. [1] G. REEB, Propriétés Topologiques des Variétés Feuilletées, Actualités Sci. Ind., 1183 (1952). Zbl0049.12602MR14,1113a
  2. [2] I. KUPKA, The Singularities of Integrable Structurally Stable Pfaffian Forms, Proc. of the Nat. Acad. of Sc., vol. 52 (1964), 1431. Zbl0137.41404MR30 #3427
  3. [3] A. S. MEDEIROS, Structural Stability of Integrable Differential 1-Forms, Thesis IMPA (1974), to appear. Zbl0363.58007
  4. [4] C. CAMACHO, On Rk ˟ Zl-Actions, Proceedings of the Salvador Symposium on Dynamical Systems (1971). Zbl0274.58006
  5. [5] J. PALIS, On Morse-Smale Dynamical Systems, Topology, (1969). Zbl0189.23902
  6. [6] M. C. PEIXOTO and M. PEIXOTO, Structural Stability in the Plane with Enlarged Boundary Conditions, Ann. Acad. Bras. Sci., vol. 81 (1959), 135-160. Zbl0107.07102MR21 #5794
  7. [7] J. SOTOMAYOR, Generic One Parameter Families of Vector Fields on Two-Dimensional Manifolds, Publ. Math. 43, IHESc. Zbl0279.58008
  8. [8] M. W. HIRSCH and C. C. PUGH, Stable Manifolds and Hyperbolic Sets, Global Analysis, Proc. Symp. in Pure Math., vol. XIV, AMS (1970). Zbl0215.53001MR42 #6872
  9. [9] P. HARTMAN, Ordinary Differential Equations, edited by John Wiley and Sons Inc., 1964. Zbl0125.32102MR30 #1270
  10. [10] C. CAMACHO, Structural Stability of integrable forms on 3-manifolds, to appear. Zbl0391.58013

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