A note on strange nonchaotic attractors
Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 139-148
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ ${\mathbb T}^1 × ℝ_+$ 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 ${\mathbb T}^1 ×ℝ_+$. 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 ${\mathbb T}^1 × ℝ_+$ is $Γ̅$, but for a residual set of points in ${\mathbb T}^1 × ℝ_+$ 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.
@article{10_4064_fm_151_2_139_148,
author = {Gerhard Keller},
title = {A note on strange nonchaotic attractors},
journal = {Fundamenta Mathematicae},
pages = {139--148},
publisher = {mathdoc},
volume = {151},
number = {2},
year = {1996},
doi = {10.4064/fm-151-2-139-148},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-151-2-139-148/}
}
TY - JOUR AU - Gerhard Keller TI - A note on strange nonchaotic attractors JO - Fundamenta Mathematicae PY - 1996 SP - 139 EP - 148 VL - 151 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-151-2-139-148/ DO - 10.4064/fm-151-2-139-148 LA - en ID - 10_4064_fm_151_2_139_148 ER -
Gerhard Keller. A note on strange nonchaotic attractors. Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 139-148. doi: 10.4064/fm-151-2-139-148
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