ArticleOriginal scientific text
Title
A note on strange nonchaotic attractors
Authors 1
Affiliations
- Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, D-91054 Erlangen, Germany
Abstract
For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties:
1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in . The set {θ:ϕ(θ) ≠ 0} is meager but has full 1-dimensional Lebesgue measure.
2. The omega-limit of Lebesgue-a.e point in is , but for a residual set of points in the omega limit is the circle {(θ,x):x = 0} contained in Γ̅.
3. Γ̅ is the topological support of a BRS measure. The corresponding measure theoretical dynamical system is isomorphic to the forcing rotation.
Bibliography
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