Weak and continuous equivalences for families on line diffeomorphisms. (English) Zbl 0641.58037

Roussarie, R.

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

MSC:

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

Keywords:

topological equivalence; line diffeomorphisms; Newhouse-Palis-Takens; Hopf-Takens bifurcations of vector fields in the plane

Citations:

Zbl 0621.00019