Abstract
The simplest patterns of qualitative changes -bifurcations- located around a compact two dimensional submanifold, that occur on smooth one-parameter families of vector fields on a three dimensional manifold, are studied here.
Keywords
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Chincaro, Bifurcação de Aplicações de Whitney. Tese IMPA, Rio. (1979).
P. Percell., Structural stability on manifolds with boundary, Topology 12 (1973), 123–144.
Peixoto e Peixoto., Structural Stability in the plane with enlarged boundary conditions, Anais da Acad. Bras. de Cs. 31, 1959.
[S1] J. Sotomayor., Generic one parameter families on two dimensional manifolds, Publ. Math. IHES., vol. 43 (1974).
[S2] J. Sotomayor., Structural stability in manifolds with boundary, in “Global Analysis and its Applications”, vol. 3, pp. 167–176, IEAA, Vienna (1974).
M.A. Teixeira., Generic bifurcations in manifolds with boundary, J. Differential Equqtions 25 (1977), 65–89.
R. Thom., Ensembles et Morphismes Stratifiés, Bull. of the American Math. Soc., v. 75, no 2 (1969).
S.M. Vishik., Vector fields near the boundary of a manifold, Vestnik Moskov. Univ. Serv. I, Mat. Meh., 27, 1 (1972), 21–28.
H. Whitney., Elementary Estructure of Real Algebraic Varieties, Ann. of Math., 66, (1957).
V.I. Arnold, On local problems of analysis, Vestnik Moskov. Univ. Ser. I. Mat. Meh., 25 (1970), 52–56.
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Sotomayor, J., Teixeira, M.A. (1988). Vector fields near the boundary of a 3-manifold. 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/BFb0083073
Download citation
DOI: https://doi.org/10.1007/BFb0083073
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50016-2
Online ISBN: 978-3-540-45889-0
eBook Packages: Springer Book Archive