WIAS Preprint No. 77, (1993)

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).

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