Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-27T22:42:57.164Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability and regularity in bifurcations of planar vector fields

Published online by Cambridge University Press:  14 November 2011

J. Sotomayor
J. Sotomayor
Affiliation:
IMPA, Estrada Dona Castorina 110, Rio de Janeiro, R. J. 22460, Brazil
Get access Rights & Permissions [Opens in a new window]

Synopsis

Bifurcations appearing in generic one-parameter families of vector fields on a compact planar region are conceptually characterised in terms of their stability and regularity properties.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 3-4 , 1989 , pp. 243 - 256
Copyright
Copyright © Royal Society of Edinburgh 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Andronov, A., Leontovich, E. et al. Theory of bifurcations of dynamic systems in the plane (Jerusalem: Isr. Prog. Sov. Transl., 1971).Google Scholar
2Boyd, C.. On the structure of the family of Cherry fields on the torus. Ergodic Theory Dynamical Systems 5 (1986), 27–46.Google Scholar
3Lasalle, G.. Une démonstration du theoreme de division pour les fonctions différentiables. Topology 12 (1973), 41–62.CrossRefGoogle Scholar
4Melo, W. and Palis, J.. Geometric Theory of Dynamical Systems (Basel: Birkhauser, 1982).Google Scholar
5Peixoto, M. C. and Peixoto, M. M.. Structural stability in the plane with enlarged boundary conditions. Anais Acad. Bras. Cien 31 (1959), 135–160.Google Scholar
6Sotomayor, J.. Curvas definidas por equacoes diferenciais no piano (Rio de Janeiro: IMPA, 1981).Google Scholar
7Sotomayor, J.. Generic one parameter families of vector fields on two dimensional manifolds. Publ. Math. IHES 43 (1974), 5–46.CrossRefGoogle Scholar
8Teixeira, M. A.. Generic bifurcations in manifolds with boundary. J. Differential Equations 25 (1977), 65–89.Google Scholar
9Teixeira, M. A.. Generic bifurcations of certain singularities. Boll. Un. Mat. Ital. (5) 16-B (1979), 238–254.Google Scholar
10Vegter, G.. The preparation theorem for differentiable functions and its applications (Lecture Notes, University of Groningen, Holland, 1981).Google Scholar