zbMATH — the first resource for mathematics

Weak and continuous equivalences for families on line diffeomorphisms. (English) Zbl 0641.58037
Dynamical systems and bifurcation theory, Proc. Meet., Rio de Janeiro/Braz. 1985, Pitman Res. Notes Math. Ser. 160, 377-385 (1987).
[For the entire collection see Zbl 0621.00019.]
A topological invariant for the continuous equivalence of families of line diffeomorphisms is constructed based on phenomena of rigidity for the generic one parameter family, found by Newhouse-Palis-Takens and also on the Mather invariant for interval diffeomorphisms. This gives rise to moduli for Hopf-Takens bifurcations of vector fields in the plane, when the number of parameters is greater than four.
Reviewer: R.Roussarie

37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
34C25 Periodic solutions to ordinary differential equations