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Bifurcationss of codimension one singularities of tangent vector fields on Whitney's umbrella

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1331)

Abstract

In this paper we classify the codimension one singularities of tangent vector fields on Whitney's umbrella and we give generic models for their bifurcations.

Keywords

  • Vector Field
  • Implicit Function Theorem
  • Central Manifold
  • Local Homeomorphism
  • Tangent Vector Field

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was partially supported by FONDECYT'S Project N° 1190/85.

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References

  1. F. Dumortier., Singularities of vector fields. Monografías de Matemática N° 32. Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brasil.

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  2. C. Gutiérrez-J. Sotomayor. Stable vector fields on manifolds with singularities, Proc. London Math. Soc. Vol. XLIV, July 1982, pp. 97–112.

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  3. M. Wallace., Caracterización de los campos vectoriales analíticos de ℝ3, tangentes al paraguas de Whitney, Notas de la Sociedad de Matemática de Chile (to appear).

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© 1988 Springer-Verlag

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Billeke, J., Wallace, M. (1988). Bifurcationss of codimension one singularities of tangent vector fields on Whitney's umbrella. In: Bamón, R., Labarca, R., Palis, J. (eds) Dynamical Systems Valparaiso 1986. Lecture Notes in Mathematics, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083062

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  • DOI: https://doi.org/10.1007/BFb0083062

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50016-2

  • Online ISBN: 978-3-540-45889-0

  • eBook Packages: Springer Book Archive