Positive quadratic differential forms : linearization, finite determinacy and versal unfolding

Carlos Gutierrez; Victor Guíñez

Annales de la Faculté des sciences de Toulouse : Mathématiques (1996)

  • Volume: 5, Issue: 4, page 661-690
  • ISSN: 0240-2963

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Gutierrez, Carlos, and Guíñez, Victor. "Positive quadratic differential forms : linearization, finite determinacy and versal unfolding." Annales de la Faculté des sciences de Toulouse : Mathématiques 5.4 (1996): 661-690. <http://eudml.org/doc/73399>.

@article{Gutierrez1996,
author = {Gutierrez, Carlos, Guíñez, Victor},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {singularity; finite determinacy; versal unfolding; positive quadratic form},
language = {eng},
number = {4},
pages = {661-690},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Positive quadratic differential forms : linearization, finite determinacy and versal unfolding},
url = {http://eudml.org/doc/73399},
volume = {5},
year = {1996},
}

TY - JOUR
AU - Gutierrez, Carlos
AU - Guíñez, Victor
TI - Positive quadratic differential forms : linearization, finite determinacy and versal unfolding
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1996
PB - UNIVERSITE PAUL SABATIER
VL - 5
IS - 4
SP - 661
EP - 690
LA - eng
KW - singularity; finite determinacy; versal unfolding; positive quadratic form
UR - http://eudml.org/doc/73399
ER -

References

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  2. [DRS] Dumortier ( F.), Roussarie ( R.) and Sotomayor ( J.) .— Generic3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case, Erg. Theory and Dyn. Syst.7 (1987), pp. 375-413. Zbl0608.58034MR912375
  3. [Gu1] Guíñez ( V.) . — Positive quadratic differential forms and foliations with singularities on surfaces, Trans. Amer. Math. Soc.309, n° 2 (1988), pp. 477-502. Zbl0707.57014MR961601
  4. [Gu2] Guíñez ( V.) .— Nonorientable polynomial foliations on the plane, J. Differential Equations87 (1990), pp. 391-411. Zbl0722.57011MR1072908
  5. [Gu3] Guíñez ( V.) . — Locally stable singularities for positive quadratic differential forms, J. Differential Equations110 (1994), pp. 1-37. Zbl0812.58003MR1275745
  6. [GS1] Gutierrez ( C.) and Sotomayor ( J.) .— An approximation theorem for immersions with stable configurations of line of principal curvature, Lecture Notes in Math.1007, Springer (1983), pp. 332-368. Zbl0528.53002MR730276
  7. [GS2] Gutierrez ( C.) and Sotomayor ( J.) .— Structurally stable configurations of lines of principal curvature, Astérique98-99 (1982), pp. 195-215. Zbl0521.53003MR724448
  8. [HPS] Hirsch ( M.), Pugh ( C.) and Shub ( M.) .— Invariant manifolds, Lecture Notes in Mathematics583, Springer Verlag1977. Zbl0355.58009MR501173
  9. [Kl] Klotz ( T.) .- On Bol's proof of Carathéodory's Conjecture, Comm. Pure Appl. Math.12 (1959), pp. 277-311. Zbl0091.34301MR120602
  10. [Ma] Martinet ( J.) .— Singularities of differentiable functions, London Math. Soc. Lecture Notes Series58, Cambridge Univ. Press, 1982. Zbl0522.58006MR671585
  11. [SX] Smyth ( B.) and Xavier ( F.) . — A geometric estimate for the index of an umbilic point on a smooth surface, Bull. London Math. Soc.24 (1992), pp. 176-180. Zbl0763.53007MR1148679
  12. [So] Sotomayor ( J.) .- Generic one-parameter families of vector fields on two-dimensional manifolds, Publ. Math. IHES.43 (1974), pp. 5-46. Zbl0279.58008MR339279
  13. [Ta] Takens ( F.) .— Singularities of vector fields, Publ. Math. IHES43 (1974), pp. 47-100. Zbl0279.58009MR339292

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