Attractors of non invertible maps.
- Bothe, Hans-Guenter
2010 Mathematics Subject Classification
- 58F12 58F15
- Attractors, non invertible maps, solenoids
For mappings ƒ : S1 x ℝn → S1 x ℝn (n≥2) of the form ƒ ( t,x ) = (Θt,λx+v(t)), where Θ ∈ ℤ, Θ ≥ 2, λ ∈ (0, 1), v ∈ C1(S1,ℝn) we consider the open subset Sn,Θ,λ of C1(S1,ℝn) which consist of all v for which the restriction of ƒ to its attractor is injective. It is shown that for λ < min(½,Θ-2/(n-1)) this set Sn,Θ,λ is dense in C1(S1,ℝn) and that for each odd n it is not dense provided λ ≥ 64Θ-2/(n-1).