A note on strange nonchaotic attractors

Keller, Gerhard

Keller, Gerhard

Fundamenta Mathematicae, Tome 149 (1996), p. 139-148 / Harvested from The Polish Digital Mathematics Library

Résumé

For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ $T^{1} \times ℝ_{+}$ 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 $T^{1} \times ℝ_{+}$ . 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 $T^{1} \times ℝ_{+}$ is $Γ ̅$ , but for a residual set of points in $T^{1} \times ℝ_{+}$ 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.

Publié le : 1996-01-01

Zbl 0899.58033

EUDML-ID : urn:eudml:doc:212186

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     author = {Gerhard Keller},
     title = {A note on strange nonchaotic attractors},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {139-148},
     zbl = {0899.58033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv151i2p139bwm}
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Keller, Gerhard. A note on strange nonchaotic attractors. Fundamenta Mathematicae, Tome 149 (1996) pp. 139-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv151i2p139bwm/

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