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Stability of parametrized families of vector fields. (English) Zbl 0632.58026
Dynamical systems and bifurcation theory, Proc. Meet., Rio de Janeiro/Braz. 1985, Pitman Res. Notes Math. Ser. 160, 121-213 (1987).
[For the entire collection see Zbl 0621.00019.]
This paper presents some contributions to the study of global structural stability of one-parameter families of vector fields whose nonwandering set is finite on compact boundaryless manifolds. The results are an extension of those concerning one-parameter families of gradient vector fields obtained by J. Palis and F. Takens. To construct the equivalence between a given family, which is a candidate for stability, and a nearby family, compatible singular foliations and Lyapunov functions are employed.

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems
37D15 Morse-Smale systems